I wish I was kidding.

I assert that the majority of men do know a lot about doing chores but that their internal concepts of "how to do a chore" differ from their significant others'.  This isn't a problem until you leap into a situation where a chore is already started - you don't know the progress of what's going on, or what's next - all you see is a basket of rumpled clothes by the washer.  Wanting to show your wife how much you want to help out, you throw them in the washer, add detergent, and voilà: instant helpful husband!  Had you asked your s/o "hey, is this laundry in the basket clean?" you still get brownie points and the laundry isn't done twice.

What it boils down to is active, persistent communication.  When you come across a situation that you don't know about, ask!  We're ostensibly a team, right?

I'm part of the world's greatest team sport - naval aviation - and we still sometimes struggle with communication.  A large part of that is the need to consistently and reliably process large amounts of critical information in order to make a decision, which can and does result in stereotyping.  Word gets around about the guy who shuts down under pressure or the gal who is a mess on the radios and that reputation is tough to shake.  Even if you've worked extremely hard on that issue and now have it under control, the people you're flying with will operate on the assumption that you're just this close to reverting back to your earlier behavior.  Part of this is due to the primacy effect - if you've got that habit, it's going to be exceedingly hard to shake and odds are good that you'll revert back to it once you stop actively flying and start autonomously flying, such as what happens under stress.

In the training command, we stress that every flight is a new chance for success and with few exceptions it is.  A big emphasis is placed on letting students make mistakes and then learn from them - but the communication aspect is critical if the correct behavior is to be imparted.  Just doing it once won't help near as much as doing it a few times - once immediately after the mistake, once on the ground while reviewing the overall flight, and then once again on their grade sheet.

Where does this leave us with gender and stereotypes?  Communication between both parties has to be emphasized and practiced, over and over again.  It won't be second nature until you're that old couple that knows each other inside and out, but it will help everything along.

(Also, I thought that NYT article was a pretty standard overview of a relatively new phenomenon with a rather incendiary headline.)