Professor decided to be TERFy during lecture

I feel so down. My birthday is soon and I just want to be happy. She insisted that “man” and “woman” are clear-cut categories “biologically” (note that my degree program has nothing to do with biology). I tried to tell her her that even biologically, sex can be complicated.

But she struck down my attempt to explain it to her and insisted to everyone that only gender can be “culturally” fuzzy, and biological sex can never be complicated. She insisted that reproductive organs will always determine sex and that our genitals determine who is a man and who is a woman in the room.

My dysphoria is getting really bad and I lowkey felt suicidal. I just want to be happy because I’m celebrating my birthday this week. I am not a woman. When I enrolled in this school, I said I was a woman for my own safety, but the staff assured me that it was okay to officially declare myself as nonbinary on the database. I hoped that this university was a safe place for me to be out as nonbinary. I really hoped. I feel so crushed.

Edit: Hi, thank you for your comments. I just wanna clarify some more things about the situation.

There are a few reasons I feel scared/hesitant to report this incident.

1) Just a few years ago, I was going to a school that was a lot worse.

The majority of people were openly transphobic or completely ignorant to gender stuff. A former dorm-mate of mine even went on a random transphobic tirade in front of me. This school is much more diverse and open-minded generally.

2) This professor doesn't act mean or hostile.

I might feel bad if I report this because she doesn't act mean or hostile. She acts friendly. The thing is that she's just a very old-fashioned woman. I mean, it's a given that our professors are a lot older than us, the students. But she's not unusually old. In fact, she seems to be on the younger end among the professors; she seems to be in her 40s. But yeah, she's not outwardly hostile, she's just really conservative-minded.

I had a little argument with her during a lecture too a few months back. Again, the lecture was totally unrelated to it, but she randomly brought up the concept of "toxic masculinity" and said that feminists use it to make masculinity seem bad. Like, she was spouting nonsense about how feminism is bad, even though a simple Google search will tell you that that's not what toxic masculinity is about at all. Even Wikipedia says that toxic masculinity is NOT about demonizing masculine traits, but simply calling out bad behavior associated with being manly (such as misogyny). I really don't know what to do. She is friendly, even though I've shown my disapproval of her random conservative nonsense.

Thank you so much for the support. I just don't know what to do about a friendly person who's in her 40s or older, who seems stuck in her conservative ways.