i've never thought about the elements of a hate scene before, but i'll try to think of some things that might help. i'm assuming here that there's a real hatred, not just a spoiled kid's 'i hate you!' for their parents not letting her go out with the local college football team.
you're halfway there when you say 'convincing.' the hatred has to be plausible to the reader and justified in the character's mind. a character just doesn't hate for no reason, they've got a reason based in experience or have been taught that way. you've got a lot of archetypes, such as the southern/redneck bigot and the angry urban militant hating 'the man.' if there's something there to exploit, it should lessen your writing load. it's instantly believable because it's real. racial tensions are pretty easy fodder, though.
between two characters, i'd say a hate scene probably would, on average, start off with a dialogue and often ending in action. situations will vary, of course, but this seems to me that it would be the most natural way to escalate the scene because it's probably the course that happens in real life. for example, if you and your buddies were out gay-bashing, you probably wouldn't just jump out of your car and start the beating before saying, 'you gaddamn faggot!' first. granted, not much of a conversation there, but still i'd think there would be some vocalization first. i mention this because i think it's important in terms of realism.
the tricky part: you want your reader to feel that hatred, too, right? in effect, you're teaching them, or at least offering up a reason, for one person to hate another. since you want your reader to identify and relate to a character, hm, there's an interesting moral dilimma, eh? lol. here i have to agree with david, the POV is important. the cowardly thing to do is switch to the 'bad guy's' POV to avoid teaching the reader why they should hate this other character. but, hey, we're not writing a sequel to the bible here, and hate is a powerful aspect of a character most wussy writers are afraid to go to. sure, it's easy for frodo to hate orcs ~ he's got damn good reason! it's harder for other MCs to hate someone in less dire circumstances and still make that character someone the reader *wants* to identify with.
there's the rub, i think: a reader wants to identify with a character... up til that character says or does something that makes the reader realize they personally have that negative aspect. in other words, exposing the reader's foibles may risk the reader's love for the character and ultimately the story. 'oh, *I* would *never* act like that!' truth is that people only *think* they'd act/react a certain in a given situation, whether it's true or not, and that way is always the most virtuous, heroic and reasonable way possible. in real life, given the exact same situation, people may act/react much worse. but they'd never admit that, and if you show them how they possibly might, they'll disagree with it.
with that in mind, i say do it. i could be wrong. if not, you've accomplished an artistic goal if nothing else. so many stories are based on or involves a hatred that's never discussed. the hero is always justified in killing nazis. hell, they shot first! then again, the hero tends to put himself into those situations where his killing them is justified. he really wants to kill them as much a find the sceptre of destiny. indiana jones admitted it, 'nazis. i hate these guys.' great line, perfectly justifiable. so what does he do? he has a long conversation with dad, waiting for nazis to show up. he *knows* he's going to kill bad guys. he can hardly wait. and he's justified for doing it, just as i'd feel justified in the same situation.
in every scene, do you have a beginning, middle and end? do you have conflict and emotional response in all of them? i think you have to put a lot of your reader's mentality into building a hate scene. what key words would the reader have to see to get his blood pressure going? it's a conflict, so one character has to do and say what the other character doesn't want to see happen or said to him. especially when the hatred is vocalized, what gets people the most upset is where there's truth involved.
sorry, i've run out of time, i'll try to get back to this later.
