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I dunno if I'm just being unreasonable, but I'm starting to think my time is up.
I'm a first alto in my school's jazz orchestra (there's 4 alto saxophones, 2 first, and 2 second - unconventional, but we're too small a school to complain). I'm not particularly happy playing alto. Last year, I played keyboard.

I talked to my music teacher, and he said he didn't want me to play keyboard until the rest of the rhythm section settled, and we'll see. After a lot of pestering, he finally said no, don't play keyboard.

The thing is, I've been playing piano for 13 years. Once I graduate, I'm taking a keyboard to university with me, and leaving my saxophone at home. Playing keyboard for the jazz band would definitely help me learn as a pianist, but this year, that's not gonna happen.

The way I see it, if he's not gonna give me the opportunity to learn, I'm better off using that time I would be rehearsing to practice piano at home.

But am I being petty to say: if you won't let me play, I quit?

I think your band director is trying to do what's best for the band as a whole, and as he sees it, the band needs you. He's not responsible for the outside projects of each of his students, and just wants to make sure the band sounds good as-is.

A lot of students learn extra instruments on the side in my band; in fact, it's strange if there's a member of the band who doesn't play an extra instrument. I found time to learn guitar and piano outside of band, and I'm still section leader of the flute section, because I know that's where my band director thinks I should be.

Just think clearly about it. Your band director isn't intentionally hindering your learning, he just wants the ensemble to sound good as a whole.

The thing is, I know he doesn't need me. There are four alto saxophones - two too many. The other first alto, I know for a fact, is a lot better than me. There's a second alto dying to play first, if we want to keep the balance.

I know he's not intentionally trying to stop me from learning, but if he doesn't want me to fill a hole, obviously I'm not good enough. I wasn't good enough to join the pit band for the musical, either (the other first alto and a different pianist were chosen). He even allowed the flute part to be played by two flutists when two people wanted to play, but he didn't allow that for the alto part.
If I'm not good enough, I have to get better. The only way I know how to to that is to practice.

Well do you have fun in band? I mean, if you're not having fun then there's no reason to stay. I know that our band is really small too (mostly saxophones like you said), but we've all grown so close that it's like one big family now, and even though our band honestly sucks, we just can't quit because we love it too much.