No, I don't think it's arrogant to start at the top. Anyone is welcome to, and you have as much right to submit there as anyone else does.
But what will be best for you to do depends on different factors, including how rejection affects you and what you mean by the "top" markets. What genre? What are the acceptance rates and do you notice a heavy preponderance of big names or MFAs there, and how long is the wait and do they accept simultaneous submissions. How do all these factors sit with you?
If you are going to get discouraged by having your stories out for many months and in all likelihood getting rejection after rejection after rejection after rejection, there's also not a thing wrong with being more realistic and sending it to places where you have a decent shot at acceptances. Or a mix, say taking a shot at the brass ring with some stories and aiming for more likely markets with others (and hopefully, faster and accepting sim subs). Or perhaps sending a story to a top market or two, then going down a few pegs. Even the small, new publications are typically swamped with submissions and reject many more than they accept.
When a publication has a percentage rate of only half of one percent, for example, that is one in two hundred. If you've ever entered, judged, or read the entries for just about any literary contest, well, let me say there will be many good stories out of two hundred, and that's before we figure in the extra weight given to well known entrants. And many of those top magazines take many months to answer and require exclusive submission. It's not a lot of fun and of course very long odds.
I like that book about how it takes 10,000 hours to become very proficient at something. A huge factor there is motivation to keep at it. Personally, acceptances motivate me and rejections discourage me. I'll write ten times more at least if I get a steady stream of acceptances. And of course writing more is how you improve. And getting those stories out is how you build your name. Many people do read publications aside from just the very top few in your category, and then there are reprints.
My advice is first, if you haven't already, get those stories critiqued (and critique other stories in return- huge learning opportunity there). Don't send anything out that's had your eyes on it only.
Second, sign up with duotrope or submission grinder.
Third, don't listen to absolutes. Ever. Ha ha.
Good luck!
I don't think any of this is good advice. It's plan to fail advice. Fast response times and sim subs are just silly things to consider. Worrying about how long it takes makets to respond is a guaranteed way of killing sales.
Any market you're "likely" to sell to is a market that will probably kill your career before it even gets started. The worst thing you can list in a cover letter is several sales to markets where known names and MFAs are not the preponderance of acceptances. Such sales may cheer you up, but they look very bad in a cover letter, and are bad, if you really want to sell to top markets.
Funny things about getting critiques is that trying to find a successful writer in a big critique group is like trying to find a cavity in a hen's tooth. The worst writing I see by far is writing that's gone through a bunch of beta readers. Don't send anything out that's had your eyes only on it? Seriously? If that mattered at all, we'd have a high percentage of good writers who use beta readers. We do not. We have an incredibly high number of writers who can't write a grocery list, all of whom have been beta read to death.
No matter how much writers wish it weren't so, good writing comes from a single writer who digs down inside himself and writes from the heart. The only beta reader who can really help him is a working editor. Beta readers just turn what he writes into the same old, same old, they've read from other writers. It simply doesn't work. If it did, slush piles would be infinitely better than they are because darned near every writer in the slush uses beta readers. Except for most of the really good, original ones.
Duotrope is a good place to find markets, but using any place to see how long response time is, or what the acceptance rate is, not only won't help, it's just silly. No good market has a high acceptance rate. Selling to such markets has nothing whatsoever to do with acceptance rate, or odds, or anything else except being able to write well, and knowing what a good, publishable story is. Not submitting to a market because it has a low acceptance rate means you'll probably never be a top tier writer. The lower the acceptance rate, the better the market. And worrying about response time makes no sense at all. If response time matters to you, if you even notice it, you aren't writing and submitting anywhere near as much and a soften as you should be, especially if you buy into the 10,000 hours nonsense.
The 10,000 hours book is filled with pure nonsense, and has been proven wrong over and over, but people still cling to it because it's an excuse to still be bad at something long, long after those around you have started selling to top markets, and may even be rich and famous.
As for how rejection affects you, it's part of the writing life, and if you base submissions on how bad old rejections make you cry, you'll never get anywhere.
Aim for the bullseye! Good luck!