I doubt Nathan does that, but that is a perfect response to that nonsense!
Perhaps very I'm innocent or naive, but I hold the door open for anybody, male or female, out of politeness
As do I.
& I use a cane, so I get that a lot, & I appreciate it. But if I'm at a door first, even if I enter first, I will hold the door for whoever is right behind me. Male or female. If they are very old, infirm, pregnant or the like, I will let them enter first. Just common courtesy, which seems to be less & less common!