I wouldn't be upset about getting beat for 1st chair if I thought the one who beat me deserved it. I made the regional top honor band while she made the bottom, I made the Allstate honor band while she didn't make it past prelim auditions, and I received 1st chair in orchestra this year while she go 3rd. She always misses her partials, and still cannot play the four note solo even though she's had her music for weeks.
Skill might not be the only factor too. She takes private lessons from our assistant band director and is always buddy buddy with both of them. My band director could have something against me because I chose not to participate in the Musical pit orchestra, seeing as the rehearsals were long and frequent and I am really trying to do well in my AP classes this year. (So he really can't blame me for not doing it). I've heard from many that did do pit orchestra that she and the other player could never hit their notes and that they sounded terrible, and everyone is really confused as to how she got first chair. Don't get me wrong, she is one of the nicest people I've ever met and I could never be rude to her about any of this (I'm more angry at the directors than her), but being nice doesn't mean that you should get something you don't deserve. I really believe that I could do better and help the band more as first chair than she could (seeing as there's two horn solos that are in our contest pieces and she can't play either). How should I approach my band director about this? He's always stubborn and he says that we'll have more chair tests but that never happens. We don't do challenging at my school either. It just really annoys me that she asks me to sing the solo for her every time she can't hear what it's supposed to sound like, and I'm sitting here completely capable of playing it excellently

My advice: just go for it or, if you have one, go to the council.
I have some experience with this as well. I am quite young (16 years) but have played in my wind orchestra for over 5 years and only had 4th chair (trumpet) which mostly means low notes. A few months ago the director of the youth orchestra gathered all the older youth (so the youth who are in the regular orchestra as well) for a little talk about how things were going. One girl said "it's always the same people who get the first chair, and this way i honestly do not feel like i am learning something." Most of us agreed, as we know there are many other members, in the youth section as well, who are perfectly capable of playing a solo. But since they never played one outside of the yourh orchestra they just need a little practice when it comes to gut. So the council decided to let the youth play 1st chair during the christmas concert. However two of the elder members did not agree with this, and unfortunately, the man of the couple is the 1st chair trumpeteer and he has an ego from Earth to Mars. So i was the main victim of remarks and statements made by the couple. It almost came close to bullying. I was being called a bad trumpeteer, an idiot, and a lazy-ass, to name a few things, and temporarily quit my big band because they were in it as well and i just couldn't take anymore of what was happening between me and them. I finally confronted the woman (a sax player) together with my dad and we later went to the council. It was that moment when i found out that i was not the only one who had totally no respect for those two since the last few months, as they staid away from the christmas concert just because we played first chair, and because of the way they treated me.

Okay so this was quite a long story. Excuse me for that. But my main point is: just go for it! If you just confront the guy and tell him what you think he has to listen to you, even if he doesn't like you. And if you feel like you are the only one having problems with the first chair player or for that matter the director, just ask around a bit to people you trust. obviously not the people who are good friends with them! and if possible go to a council or a comittee because they ultimately decide what happens, not the director. If they say you deserve first chair, then the director has to put up with that. I hope that my experience helped you a bit.

I agree, just go for it. Show them you can do what you say. Actions always speak louder than words. And hopefully that favortism you talked about isn't real and only in your head.