Sexism is bad. Any reasonable person should be upset at hearing discriminatory opinions. But what about hearing people being proud or excited about their own gender?
“As a woman, I need someone to nurture.”
“I really like learning martial arts with other women.”
“My men’s discussion group helped me understand how my masculinity could be positive.”
If these kind of gender stereotypes make you furious, have you considered if you are nonbinary or trans?

Let me back up several steps. When the average acquaintance says something about their own (cis)gender identity, they are usually assuming you are a cisgender person, either a man or a woman. Bringing gender into the conversation reminds you that they are applying gendered assumptions not only to themself, but to you, and those assumptions may clash with your internal understanding of yourself.