I hold doors open for men, too.
Turnabout is fair play.
Any woman who gets all spun up over a man extending a courtesy to her needs to get her priorities straight. There's little enough courtesy in the world without punishing people for behaving themselves.
Now, preferential treatment solely based on gender is not the same thing, and I believe it's wrong. (I don't extend this to medical issues. Women shouldn't be expected to stand for long periods when they are pregnant. Men shouldn't be denied life insurance because they are a statistically poorer risk than women.)
There's nothing wrong with courtly behavior. The court generally smiled on courteous treatment of women, and just as generally frowned on knife fights among the men in the hall. :)