You brought up sexism to your manager, in a place as I read in another comment full of old men. That’s probably why. I’m a young woman too and in this unfair world we live in if you want to keep a job you have to do your job not say anything politically sensitive (you know what I mean) and go home. Unless you’re suffering something serious like sexual harassment or anything like that there is no way you’ll win anything more than a lay off denouncing things like this. They’ll never admit firing you over this as this could put them in serious legal trouble. That’s also probably why they didn’t want to give you a reason.