I know there are plenty of men who want to split domestic chores fifty-fifty and take an equal role in childrearing, and I admire them. But there are plenty more, including myself at times, who have been happy to let our spouses shoulder more than their fair share of domestic work - not because we're deliberately trying to be troglodytes, but because a good portion of domestic work is thankless and uninteresting. So we do things less often and less well than our spouses, usually unconsciously, and eventually things gravitate towards something like an eighty-twenty split. This gets us what we want, but it also gives rise to the incompetent husband stereotype that's bothering the author of this piece.
I've got no idea how to fix this soft bigotry of low expectations, if it can be fixed at all - we obviously don't mind being made fun of for our incompetence at things we don't want to do in the first place. Cultural problems are always the hardest to solve.