why someone living on their own wouldn't need those skills?

They probably would. But it's a very different statement.

In fact, shortly before I graduated college my mother said to me (a male) that I should learn to cook because it would make me more independent. She was right.

There is also some difference between learning to cook and clean for yourself and for someone else. With one, you can follow your own taste. With the other, you need to memorize typical taste.

But mostly it's a very different statement.