exercising his right to free speech. If they kicked him out of school because of what he said in the microaggression panel, that would be clear cut for him winning the case.

UVA claims they kicked him out of school because of his actions following that because they violated the code of conduct, so that wouldn't be retaliation for free speech, but instead retaliation for improper conduct.

That's where I think we're missing key information from his side of the story. If his reactions to the professionalism card were reasonable (like he got really defensive and raised his voice and maybe said a couple things that almost crossed a line) and UVA kicked him out for raising his voice and saying a couple maybe slightly inappropriate things, I could see the causal link between what he clearly should have been free to say and UVA retaliating. (And aside from the legal aspect of that, UVA would be very wrong in general for doing that.)

But if his reactions went beyond reasonable frustration and included excessive aggression and/or threats, then kicking him out wasn't because of speech but because of his actions, which seems fair especially in thinking in context of doctors. If a patient accuses you of malpractice (for example), it's fair to get frustrated and defensive and say a lot of things, but there's still a line you can't cross including threatening physical harm, etc. If you unreasonably overreact to a perceived wrong (whether real or not), there are certain professions you probably shouldn't be in, so it would seem fair for UVA to be able to kick someone out of med school for such behavior. In that case, it has nothing to do with free speech.

I would guess there is a question of whether that professionalism card itself would constitute "retaliation," but I would guess not since it sounds like the card alone doesn't automatically mean further action against the person.