In my opinion, the one point that should be DRILLED into people's' heads is the Fundamental Attribution Error (FAE). What the FAE says is that we attribute situational causes to our behavior while attributing dispositional causes to others behavior. Perhaps an example would help: I cut people off in traffic because I am late and need to get to my appointment. You cut people off in traffic because you are a self-serving, self-engaged, Republican idiot.
Why this should be drilled into people's heads is because it IS fundamental. We all do it, and we do it without even thinking about it. But, it is also an ERROR! And being an error, it gets in the way of being kind. Look at how many attribution errors are made: gays are unethical, Republicans are idiots, Baptists are self-righteous pharisees, Muslims are bellicose freaks... When we want to categorize any group of people, we start making attribution errors.
Even when we deal with single people we do this. I may be feeling ill and am being quiet, but others may think I am being either shy, aloof, or judgmental. The judgment of others has not basis in reality, but they assume it to be true. And it often becomes the basis with which future interactions are framed.
How many arguments could be saved if we give the person the benefit of a doubt? How many marriages could be saved?
I was just thinking: When we are making FAE's about the other person, they are making FAE's about us! How many conflicts are based solely on bad assumptions?