At least WolfishMusings is agreeing there is no more reason a Yid should open it for her, than she for him. Look up chivalry before opining that it is permissible for a Yid to engage in.
But I *do* hold the door for her — you missed that salient point. You said it shouldn’t be done at all. The fact that she returns the favor on occasion doesn’t negate that.
The Wolf