If a guy did that, I’d think he’s a rude prick. If I knew he did that for my supposedly fragile mental state, I’d assume he’s a rude, condescending, sexist prick.
But even the woman who is writing this would probably think, if a guy actually did it, that he’s pretending not to notice her because he despises women.
Ideally, people would use the basic principles of convenience. Shorter people should go first because they can’t see over the heads of taller people. Instead, people bring their neuroses to basic actions and confuse everybody.