The definition of someone who "can't cook" is so wide that it's sort of pointless, though.
My DM "can't cook". According to my DF, who was and is chief caterer. Cooking was never a gendered job for me growing up. Actually she is a fine cook, it's just he's better. And she likes to eat stuff he doesn't so he'd prefer to be in charge of the menu & catering and not have to be on the hook to clean up
My SIL "can't cook". She can heat up/follow instructions etc. But her DC are fine eating sandwiches, school lunches, ready meals and takeaway/meals out, or MIL will cook for them, so where is the incentive to learn?
My FIL "can't cook". When he got divorced from MIL, he found a new wife who could, so no worries. He makes an excellent cup of tea, however.
My DH "can't cook" (MIL is definitely a background factor in a lot of my examples!) He can make cheese on toast (in fact this is his go-to sole diner meal), can do eggs all ways, can stick stuff in the oven, can grill a sausage or panfry a steak, can follow a basic recipe and can totally fuck up a reasonable dish by adding a ridiculous ingredient He can feed the DC adequately well - pesto pasta peas, eggs, fishfingers/pizza/etc., wraps & sandwiches, soup & salad etc. But if he were the only parent catering it would be shit. He could choose to learn, and I hope he would, if I were not around.
I "can cook" - by which I mean I can make something balanced and nutritious out of any ingredients lurking in the fridge and the store cupboard, pretty much off the cuff and without a recipe or a plan. I care a lot that my DC eat a balanced diet - not too much wheat, not too much salt, more from scratch than from the freezer etc. But I agree with MrsHathaway who said way up thread
Cooking is such a lovely hobby and skill when you don't have to do it ten motherfucking times a motherfucking week.
I LIKE cooking. But in terms of feeding kids and a family it is a huge CHORE, and so I can see why no one in my examples above "can cook" - it's because in all cases someone else will step in and do it for them. I don't think it matters who has a penis or not, but it does matter that there is someone else assuming the burden of worrying about the nutrition. Just like cleaning the toilet or hoovering is a chore, or the laundry. If some other bugger will do it adequately then why rock the boat?
So the DC in the OP's example had nothing to fear. But I do have to agree that no one should be wearing the "can't cook" thing as a badge of pride.