It's more "don't try to force change on them". If you think you're going to 'make' your SO stop smoking, watch movies with you, or wash the dishes, you're approaching it the wrong way.
Communicate. Express what is happening and how it is affecting you, in a way that doesn't place the blame on them. (Also, they have to be mature enough not to hear it as blame. Both can be difficult, and just about impossible when your emotions are worked up.)
Then you talk about how to solve the problem. Not in a "your behavior is a problem, how do we change it" fashion, but in a "it's us against this problem" fashion.
In the article, he says "the existence of love, trust, respect, and safety in our marriage was dependent on these moments I was writing off as petty disagreements". Instead of recognizing and respecting her complaints as legitimate -- no matter how minor -- he dismissed them, and thus told her "Your needs aren't important to me".
As he also learned, petty disagreements become major problems when not dealt with. You either take care of them early, when they're still easily tractable, or you wait until they've festered and become a Major Problem. And then they're really difficult to fix.
