"To offer a perfectly healthy woman a seat simply because she is a woman, however well-intentioned, is creepy. At best, she'll think you're from another country; at worst she'll feel old, or overweight enough to be perceived as pregnant.""
It's worse. It's tantamount to sexual assault these days to offer anything to any woman. What you'll get, at best, is the insulted look of someone who thinks she's being hit on. Feh.
Not true. There are still some ladies out here who appreciate good manners. I don't expect doors to be held open for me just because I'm a woman. If I am entering an establishment ahead of someone, I hold the door open for him/her. It is just plain disrespectful to do otherwise.