Hi Amber, it’s always hard to generalize for one gender based on one’s own experience, but in all my conversations with men (we may hang out in different circles) I’ve never met one who rejected a woman because he wanted to pursue her.
In any case, I’d argue that increasingly men have no choice. Pursuing a woman is risky for a man because if he loses control for even a minute and lets his passion take control he may end up making a consent mistake and be labelled a harasser or rapist; this is true even if his intentions were purely and strictly kind. Consent is confusing and we’ve handed over defining the contours of consent exclusively to victims (usually women). When a man is confused about consent he is now also guilty of a crime.
Men who are “woke” (I hate that term, but it applies here) and have a decent sense of self preservation should NEVER pursue a woman. If he gets horny, well he can pleasure himself or seek out other men, who are relatively less likely to take offence at a misguided attempt at connecting.