True Chivalry is Never Sexist

I hold the door open for everyone, male, or female, who I meet. It becomes a pain in the neck after the fourth, or fifth, ingrate has barged through, but I do it even if I'm in a hurry.
I firmly believe that good manners make me a better person. Chivalry is just an extension of this, it costs nothing and makes the world a better place.
Chivalry is an integral part of civilisation. It isn't some medieval invention by knights, it's deeper than that.
Man developed, because our ancestors shared their good fortune with their neighbours. They cooperated to find food and protect vulnerable members of their community. It would be a shame, if we lost the benefits of chivalry through the mistaken belief that it is sexist.
I've shared most of my life with my wife, some people would consider this to be a sexist remark. 'My wife' to them implies ownership, but she refers to me as 'my husband', is that sexism too?
I would never dream of intentionally letting a door slam in her face and I hope that all of the people who say chivalry is sexist would feel the same about their friends, lovers, partners, colleagues, fellow commuters...
Why not extend this to everyone? It is only a very small step. A stranger is after all only a potential friend. It costs nothing and makes you feel good.
Go on try it.