The only thing you can do is to pull them out on it. what do you mean by showing favoritism?? Are they only paying attention to one person, or what?? if it is really bad maybe u should talk to the head of your gym or get your parents to.
I would talk to your coach about that. I would ask him/her why they are doing what they are and explain why its concerns you. Maybe they don't mean to be "picking favorites" and they are know that person more than the other people in the class. But I would talk to your coach about the matter.
When in doubt, confront them about it. Simply ask them mildly and gently. I cannot even remember how many times a young female gymnast or younger high schooler coach has complained why that I supposedly do not like them or pay attention to them.
I have been known to favor the gymnasts who work their butts off. Not the suck ups, but the gymnasts who do it for themselves and the group. I consider it as rewarding good behavior. It's great when they are not interrupting me when I'm trying to explain the lesson plan in 45 seconds or keep up on disrupting the W/U by being too chatty.
Sometimes certain gymnasts just bond better with certain coaches. This has to be kept a careful eye on. Sometimes, they remind of me or they understand my personality or my method more. Sometimes, apparently I'm just a likeable or funny guy. Sometimes they like the fact that I will not sugar coat it or that I recognize when my something is not right ( physically or mentally/emotionally ). Sometimes they just don't like me all that much while they adore another coach. Perhaps it's those days I forget to shave or when I insist on wearing my hawaiian shorts and shirts.
If, however, they disregard or fail to explain why when you call them on this; it might be time to bring this up to your parent and see that coach's boss or management. If they're an owner, well there is no going higher up the rank. If however, it's bad enough you need to escalate it to asking another of your coaches or the head compulsory/optional or Team Director; you just might have to do it.
And sometimes coaches just have bad days. However, there should be something of a dialogue between coach and gymnast. Even if it's of the old school manner, there should be something of some sorts.
I think all coaches are guilty of showing favoritism at some time or another, and most of the time, they might not even be aware of it. The best thing to do is talk to your coach, or have a parent talk to him/her. My daughter had a coach that sometimes did that, and I brought it to her attention a couple of times. Luckily, she was very understanding. One thing she told me was that it really helped to give her specific examples of how she appeared to be favoring others. Don't just say, you like so and so better and favor her. Tell her specific things she said, comparisons she made, or compare the time she spent one-on-one time with so and so while you were struggling with a skill 10 feet away. Maybe she doesn't realize that you are sensitive about certain things said, or maybe she didn't realize that she spent too much time on one girl. Sometimes the squeaky wheel gets the oil! Thus, the quiet kids get ignored. If you ask in a way that lets her know you are concerned, and not accusing, then she/he should be glad to help you. I hope your coach will listen and work with you to correct this problem. Not all coaches will. We dealt with another coach that also did that, and this could not be corrected, even through the gym owner. In that case, we had no choice but to go elsewhere. Good luck, I hope it works out for you.
I have to agree with gymnomore, quiet gymnasts sometimes just get overlooked. My dd is so quiet, she'd like to try more skills, get spotted more or just get noticed. But, she'll never say a word to the coaches, meanwhile her team mates call the coach over, ask to get spotted, seen etc. So guess what, she feels as though the coach has favourites, but having been in the gym, I see that it's often the squaky wheel that gets the grease.
I also like the idea of detailing specifics to a coach, a coach cannot remember everything.