In my opinion, chivalry is a kind act. Our problem is we are overly sentimental. If we are so confident in ourselves and have no need for a partner, why do we partner up?
Women's emotions are conflicting. We want to be loved and cared for but when our partner shows their kindness in their way, we misinterpret their intentions.
I'm still trying to figure out why men should even bother being kind to women. Nowadays, it seems every act of kindness is sexist.
You are a grown woman, you could have walked into your car the moment you felt oppressed but you didn't, why? When he said he was running late and suggested to get you a cab, you could have rejected his suggestion and gone home by yourself but you didn't, why?
I have read some of your stories about your husband and I do admire your relationship with him. Men aren't minded readers. I'm sure he had no idea you were offended by his gesture.
And if that's the case, then you can't accuse him of being sexist. As for your question if he would have done the same for a man. Well, I'm sure if he were having a sexual relationship with the man, he would have driven his mate too.
If it was a woman he had no sexual connection with and she insisted on driving herself, I'm pretty sure he wouldn't have argued her driving skills either.
How we treat the people we love is always different from how we treat everyone else.