It’s inappropriate if it’s inappropriate. Not that hitting on a woman is inappropriate in itself.
Think of it the other way around: You send an email trying to quickly schedule an appointment with someone, and they reply with a time, and flirt with you. It’s weird because there’s no context for that.
There's a TV show starring Stephen Merchant from a few years ago called "Hello Ladies", in which he plays a character who is constantly hitting on (and being rejected by) models and actresses. He has a frequent complaint when he gets shut down for behaving inappropriately: "What are the rules?!?"
It's frustrating for people who are less socially adept to learn that, in some cases, there are no hard and fast rules.
Competition strategy. The more people you can convince that they shouldn't hit on women means fewer people hitting on women, which improves the chances for those who hit on women.
Same reason 'slut shaming' is a thing, which is the same thing, just from the other point of view. The more people you can convince to not accept the advances of others means more opportunity for those who do.
Think of it the other way around: You send an email trying to quickly schedule an appointment with someone, and they reply with a time, and flirt with you. It’s weird because there’s no context for that.