Her point is that men are fine "taking care of themselves" when they are sick and that women should learn to do the same - even though as you and I both pointed out that probably means everything goes to hell because he's likely not going to pick up the slack.

She's saying the issue is with women, and you and I are both saying it's with guys who won't take care of the woman in their life the way he expects to be taken care of. That's not making her point even one little bit, and from the rest of your comment, you seem to agree with me.