Yes, I do feel it creates a negative, not sure if arrogant is the right word, tone.
Why are you even going into events in the past, regarding your moving, changing schools etc.?
If you were truly making the best of the situation, you wouldn't even have to bring it up.
Even your response to me is, well, in this case, arrogant. Telling me I'm terribly wrong if all I got out of it was xyz. You asked for critiques, and you make excuses.
I'm voicing my opinion that you shouldn't talk about how you really wanted this other school, but since you can get the degree you've decided you want from UT, then it's ok, you guess. Sure you use words like "what better place than UT" but things you said before that makes that ring false.
It's like saying "I was really in love with this great person, but they didn't accept me, so I guess you'll do."
By all means explain how you have the disciple, drive and passion, but do so by concentrating on the positive.
In particular, I wouldn't mention I was "furious" about having to move. That would make me wonder what other things you're going to get furious about.
In fact, of the 4 paragraphs, the first, third and fourth are fine. The third one doesn't put you in a very good light.
My critique is to rewrite it and leave off the high school kid stuff, how you had to move, how you were furious.....and for God's sake, leave off the "deep in the heart of Texas" stuff. That sounds so provincial.
Keep in mind the people that will be reading your essay won't all be like Jespah. They might be more like me, at least some of them. Some will be worse.