I'm totally sexist and racist but I'm not sexist or racist but...
Alot of women don't built or earn skills or character because they don't have to. Everything will be handed to them. If you do in any way try to teach her to cook; you are being rude, calling her stupid, and saying you hate her, in her mind anyway. So that puts her off learning anything even more.
It's very frustrating to be in that situation. You are right to feel that way and there is no good answer to your problems better than "learn to deal or force her away." In the big picture of a relationship, lunch shouldn't be a deal breaker but the overarching behavioral patterns we both described may be. You both seem unwilling to have an honest and open relationship nor change and grow together, meaning you will only grow apart.
A good relationship means doing the hard work, sometimes (tactfully) informing the other person that "you act like such an idiot and it makes me want to walk out and leave your fat *** to wallow in your mess." We know that "upsets" them so we don;t until we do burst out in so many words. Until then, the hide in the bedroom until they know we miss their companionship enough to not care about the original issue. Ain't love grand?