I am going to tell you the same thing I told my husband about him not cooking. It has nothing to do with you being a female, but to do with the ability to be self sufficient. There will come a time in your life when you wont have other people cooking for you, and eating out is massively expensive compared to cooking at home. You NEED to learn how to cook so you can feed yourself something more than a dry sandwhich and ramen when that time comes.
As far as the go back to the kitchen comments, that is the lingering effect of sexism. Back in the days before modern medical care and towns with significant populations, children were necessary to secure the well being of the family - boys to help plow the fields, girls to bring to marry off. So, without birth control and the actual necessity of having children, women were pregnant often. Even in the not so distant past, my grandmother had 10 siblings. That was common. My parents had 4 siblings. That was common. I was an only child. Some what less common, but the avg family only had 2 kids around that time. Without all the medical care and knowledge we have, they put women on bed rest or doing house work when able while the men went out and did all the work that was thought to have been unsafe for the pregnant woman - and honestly, at that time, a lot of that work would have been unsafe for her. Today the pregnant woman can do just about anything, but that is with medical care and monitoring the baby. It takes time to change the social norms of a society. You have to remember that what is mostly off color humor today, was life for a grand parents, great grand parents, etc.
I like a messy room too. It sucks that your mom puts a gender on that, but the truth be told... your life habits are being built now. If you keep a messy room now, you will likely keep a messy house when you are older. Gender expectations aside, a messy house will cause you to be more depressed, and cause peers to look at you negatively.
Your mom is behaving as if she were sexist, and maybe she is. But while it feels harsh on you right now, YOU are the one who is going to be more self sufficient when you get older, not your brother. That ability is priceless.