Actually Cindy, It's been my experience that women don't want the floor mopped differently, they want the floor mopped THEIR way.
After 20 years of helping around the house and having her come back and complain that I'm stupid because I didn't do it the way she wanted and having her do it all over again, after 30 years of marriage, I don't even try anymore.
Why bother if she's just going to do it all over again anyways???
Well, you know what they say: if you want something done right, do it yourself.
It also seems to be that part of the problem is that when the woman decides something needs done, she seems to think that it needs to be done right now. The man usually seems to think that he should do it when he's so inclined.
I can understand the resistance to your efforts not being good enough. What I don't understand is having an "approved" way of mopping the floor. I'm so non-focused on housework I didn't know there WERE different ways.
The best way to not have her ask you to do the house work is simply screw up the job. i.e. bleach in the laundry. She'll never ask you to do it again after that.
Yardwork, car work, housework.... it is all work. I hate mopping. I like mowing. We just switch at times. If I need something I ask. If my husband isn't interested I do it myself or hire someone. I try to do everything he asks though because he doesn't ask me to do much, unless it is really important. It took a lot of fights and power struggles for us to get here though. Hopefully things will get better for you too.
"No. Women just want the floor mopped differently"
When my son got married he told me that his mate was always on him about how he did the floor and other wifely duties. He asked why. I told him this was the way women established control. Furthermore, they expected you to like it. He's still not caught on, but what can you expect after 15 years or so? He got hardwired wrong. :-)