I’ve never heard anyone say either of those things but I don’t have an argument against the first one based my understanding of gender.

I think that parts of your statement are likely correct but I doubt a lot of it. The comment you replied to was correct though it is likely more nuanced. That is where your point could play in (which is what enables much exaggeration used by opponents) but your examples show me that you are quite biased (not that I am not) and not necessarily part of those who would be willing to listen to the whole thing.