the one I think of immediately is that my dad would always say “stop being such a girl” when I complained about things. I picked up the phrase when I was young without thinking about it
then I said it to someone in elementary school and they said “what’s wrong with being a girl” and I was like wait yeah wtf why am I saying this
Yeah it's an odd one alright but as you said very common.
I think you're right in that it's seen as a feminine thing to do. Weird stuff tbh.