I know I answered on this thread already a few years ago, but the more I consider the question, the more problems I see with the implication that humans are inherently bad and "animals" are inherently good.
Firstly, we are animals. This distinction between "humans" and "animals" is an artificial one. We are a species of great ape and just as animal as any other animal. We are actually more cooperative and altruistic than the other species of great ape - even bonobos (though bonobos are admittedly a fair bit more peaceful than common chimps). We ARE animals that have been "uplifted" (via evolution by natural selection in environments where there's a selective advantage to higher levels of intelligence) to our level of intelligence. We are what happens if a great ape lineage evolves higher levels of intelligence.
Secondly, many types of violence in humans are the same as what's found in other primate species including chimps and bonobos. This would be various types of interpersonal violence such as bullying (especially the high school types of bullying where a group of kids bully another kid by a combination of social exclusion and systematic small acts of violence). Also, a stronger individual bullying a weaker individual into giving them something. Baboon society is like if you take the most cliquey high school social group and then have violent gang leaders in charge of them. When humans behave in these ways, it's because we're social primates and those behaviours evolved long before our intelligence did. Also, while bonobos are less aggressive than common chimps, they are still known to bully each other in this same high school cliquey kind of a way, so be careful of any assertions that they are totally peaceful, non-violent, etc.
Hostility to those outside the group is another trait that we share with chimpanzees. A male common chimpanzee who wanders into the territory of another group is likely to be beaten to death. Females who come from other groups are accepted because they are potential mates. Humans do this as well - sometimes on a much bigger scale in a more organised manner due to our higher intelligence - but it too comes from being social primates and is not uniquely human. Also, very importantly, there are countless examples of when humans DON'T do this. There are so many examples of human men being among strangers and not being beaten to death. Generally, groups of human men greet unknown human men with friendliness or indifference (depending on the situation). Occasions when they get beaten up are the exception, and in a great many cases, humans who beat up other humans are punished by the majority in their social group (e.g. being arrested, put in jail etc). The human smile is evidence of us evolving to be more friendly to strangers. The smile evolved from the facial expression for fear. At some point in our evolution, groups of humans/hominins recognised that if the stranger was afraid of them, they were not a threat. So displaying a fear grimace to strangers resulted in being treated in a friendly manner. Over enough time, this evolved into the human smile. The fact that we've evolved an entirely new expression (as opposed to merely just a tendency to display a fear grimace to indicate peaceful intentions) suggests this started happening early on in our evolution, though as it doesn't fossilise you can't put a date onto it. But it is an example of humans evolving to be less aggressive and more friendly than other great apes.
Another example of natural selection in favour of less aggressive individuals - in particular less aggressive males - is seen in the current theories about how early hominin (human lineage) ancestors split from early panin (chimp/bonobo lineage) ancestors. The starting point was a system similar to many primate social groups including common chimps where male-male aggression levels were quite high and males competed with males for access to females, doing dominance displays and having large canines to indicate their prowess, and mated with the most fertile-looking females when they were ovulating (females having obvious sexual swellings when they're ovulating) without pair bonding, females only mating when they're fertile - the chimp/bonobo lineage continued in this fashion (though much later on bonobos went down a different trajectory), while the hominin lineage took a different strategy - less aggressive males seeing out less obviously fertile females and forming lasting pair bonds, through the provision of food, friendship and protection, while females sought out less aggressive males with smaller canine teeth, i.e. less aggressive/more co-operative. This explains a number of oddities about the hominin lineage, including the loss of large canines, hidden ovulation in females, breasts that permanently look like they're lactating (i.e. not currently fertile), mating at any time of your menstrual cycle, sex for pair bonding rather than just reproduction, and bipedalism (to carry food to give to your mate). The advantage for males is less competition from other males for his chosen mate - she doesn't look fertile so other males don't try to mate with her - and better chances of the offspring surviving due to greater paternal provision. The advantage for females is the greater paternal provision meaning better chances of the offspring surviving, plus someone to look after her and provide food for her at the vulnerable stages of pregnancy, childbirth and early infancy. In terms of humans evolving to be less aggressive and more co-operative than other great apes, in this scenario, you have selection pressure in favour of lower aggression and greater cooperation. This all happened long before humans started on the trajectory of greater intelligence, as hominins were already fully bipedal and had lost the large canines of other primates long before humans evolved - large cranial capacity is one of the defining features of early humans, so this happened before brains got any bigger than chimp/bonobo brains.
Evidence of humans evolving greater levels of compassion and co-operation along with greater levels of intelligence can be found in the fossil record. The earliest example I'm aware of is from 1.8 million years ago, the skull of a toothless old woman found in Dmanisi, Georgia (in Europe) - the amount of wear on her jaws shows she lived for a couple of years after losing her teeth. Someone looked after her, likely pre-chewing food for her so she could eat (food during the lower palaeolithic era would've been raw and unprocessed and much harder to eat without teeth than cooked/processed food). The fossil record is full of examples of individuals surviving with healed injuries and/or medical conditions such as arthritis, or after losing all their teeth, which would require someone to look after them. The whole evolutionary trajectory humans were on that led to greater levels of intelligence required greater levels of co-operation and sharing, especially sharing of information and teaching each other skills. It comes as a package. There's no selective advantage to higher intelligence and more complex language if you're not working closely with other humans to share knowledge and build a culture that gives you a greater ability to survive.
Next, the implication that all humans are selfish, greedy and destructive is a very ethnocentric one. Spend some time learning about any modern hunter-gatherer population and you'll find that they are not selfish, greedy or destructive. While some level of interpersonal violence is found in all human societies, on the whole they are co-operative, compassionate and place a great emphasis on sharing food, resources etc fairly. Hunter-gatherer populations being like this are more evidence that humans have evolved to be more co-operative, compassionate and caring. In the modern world, hunter-gatherers may appear to be the exceptions on the fringes of other human societies, however when you consider how long humans have existed - the earliest humans lived about 2.3 million years ago - and that agriculture only started 10,000 years ago and industrial society only in the last couple of hundred years or so, and there are human populations who've never been anything other than hunter-gatherers, hunter-gatherer societies should be considered default for humans.
If you remove the ethnocentricity inherent in the question, what you're left with is asking why some agriculturalist and industrialist humans are greedy, selfish and destructive. That is a very complex issue, but the ability to accumulate wealth in agriculturalist and industrialist societies is a major factor, or more specifically, the ability to use accumulated wealth to wield power over others. There are circumstances that can bring out the worst in humans. Recently I watched a documentary about the Roman emperor Caligula. A combination of being given absolute power, the age at which he was given such power (early 20s), plus factors in his childhood (a combination of being a spoilt child and various horrible tragedies like his whole family being murdered by other power hungry people) led to him achieving horrific levels of sadism, debauchery and hunger for power (at least until he was assassinated by the Pretorian guard that were supposed to protect him because they were utterly sick to death of him, along with the Senate and most of Rome's upper classes). If he'd had a normal childhood and not been given that power, would he still have been so horrible? The wrong set of circumstances can make humans do horrifically bad things, but that is not human nature, it's a corruption of human nature. There are factors within larger agricultural societies (late neolithic onwards) and industrial societies that create the conditions where such monstrous people arise. Power corrupts. This is **NOT** the default for humans. There are also factors that can lead to whole populations doing the bidding of such monstrous people, carrying out large scale human rights abuses. This is something that industrialist humans need to examine carefully to prevent the circumstances arising that can result in such things happening.
The fact that people are so horrified by the behaviour of these extremely corrupt and nasty people comes from the fact that such behaviour isn't normal. If it was normal we'd all be like Caligula and be going around doing horrific things to each other on a daily basis, but we don't. On a daily basis, we are co-operative, considerate, kind and are prone to being altruistic. So again, the default for humanity is friendly and co-operative with altruistic tendencies. But there is a necessity for larger societies to keep a close eye on what's going on and preventing circumstances that can result in human rights abuses. This is within our capabilities, and the fact that large numbers of people want this to happen is more evidence that the default mode for humans is nice.
So what would happen if other animals evolve human levels of co-operation? Well, if they didn't evolve from great apes they're not going to behave like great apes. They're going to retain a lot of the wiring from whatever group they're part of. You would have to answer this question separately for each different type of animal. What if wolves evolved to be as intelligent as humans? What if a cat species evolved to be as intelligent as humans? What if chickens evolved to be as intelligent as humans? You'd get a different answer every time. This idea that "humans are bad" and "animals are good" is wrong, because modern humans are one species of animal and every animal species is different. If any other animal evolves to be as intelligent as us, what they are like that the end of the process will be due to a combination of the traits of the animal they evolved from and the traits that were selected for as they evolved higher intelligence. Personally I think it's inevitable that higher levels of co-operation and altruism will evolve alongside intelligence. If their starting point is an animal that's less aggressive than great apes, the result could be a less aggressive animal than humans, but that wouldn't be a foregone conclusion. The question of whether, having evolved that level of intelligence, they are able to build societies that are fair and compassionate is going to depend on them when they get there. They'll be subjected to all the same issues that humans are subject to. Building a fair and compassionate society isn't beyond the capabilities of humans. Once you get to that level of intelligence, you have the capacity to make choices and try to understand the consequences of those choices. Chances are any intelligent species will succeed sometimes and fail at other times. Ultimately I think humans are currently on a trajectory to build a better world, but the biggest barrier is how we deal with very rich people who hoard wealth and refuse to accept responsibility to the damage they do to society, people and the environment. "All that is needed for evil to thrive is for good people to do nothing." Implying that humans are inherently bad is a bit of a cop out to be honest. We aren't inherently bad, but we industrialised humans could be doing a lot better. C- must try harder.