Our parents grew up with a very different education; we can't blame them for their gendered ideas about cooking and chores. We can try to actualize them, for sure, but they are entitled to their opinions and preferences.
Dividing chores THEY have to do based on gender is one thing, but when it comes to their sons and daughters, especially after they are over the age of 21, it is a completely different scenario. Technically, the daughter in this story is a full-grown adult and not obligated to do what her mother says, but of course, when you live under someone's roof, only their rules matter.
Sadly, the only solution to problems like these is moving out; there is no use in trying to explain dated binarisms to adults who don't mind listening. When you're old enough, you should search for your own independence and, hopefully, resume cooking in an environment where you're not obligated to feed other people only because of your gender.
I remember when I lived with roommates, cooking was a nightmare. I never wanted to go to the kitchen because there was always someone watching what you did, or someone had left dirty dishes in the sink.
I had to wait until I got my own apartment to rediscover cooking. I could finally use the kitchen without someone watching; I could experiment without fear of failing, and I could take my time to wash everything I'd used. So I'd encourage everyone who feels uncomfortable at home to find their own place. I know it's not simple, and I know this economy is tough, but with time, anyone can do it. You just have to take it one step at a time!
Do you think the daughter should move out? Or does talking to her mother make sense in this scenario?