I never did anything about that firing because it was a s****y job, but I do remember thinking "You can't fire me for not liking me!" Yes, that can be the reason, but you can't say it. You need to do the employment version of "It's not you, it's me" and lie to my face. God, anything but the truth. The truth is surely not legal in this case.
Except it is.
Not unlike break times, rules governing reasons for dismissal are generally not covered on a federal level. You're very likely an at-will employee which means your employer can end your employment at any time, for any reason. The caveat to this is only federally protected anti-discrimination type reasons or retaliation or anything illegal. So you can't be fired due to age or ethnicity or any of the small number of protected classes, or because you refused to set your co-worker on fire. But, considering you could be fired for simply not being likable, most employers who are going to discriminate against you will probably not say so. And if your employer wants to fire you because they feel like three monkeys in an overcoat will do a better job, they probably can.
I've known tons of teenagers who lost their s**t after being fired, claiming, "This is discrimination! I'm going to sue!" But the reality is, unless it's really, really transparent, they can fire your ass and put "just because" on the pink slip. And there's not a goddamn thing you can do about it.