A few years ago, there was a traffic safety slogan: "On the road, don't be right, be smart". The point was that even when you are right, sometimes it's more important to think about what you are doing. For example, even if you have right of way, you should look and make sure other cars aren't going to hit you.
I was reminded of this by recent discussions on two email lists to which I subscribe. In both cases, someone made a comment, and some list members disagreed with what was said, and this led to many people expressing their opinion, taking sides, trying to produce evidence that they were right, and even insulting each other (intentionally or accidentally). This sort of behaviour creates a bad atmosphere, and sometimes causes some list members to unsubscribe. Although it's easy enough to delete messages in a thread that has become a waste of time, it can still be annoying to know that this is going on within the group.
In the first case, the disagreement was over a point of procedure within an organization. It turned out that different regions have different rules, and that even given the rules that would have made the original comment "right", people disagreed with the way it was expressed.
The second case was a major argument about language usage. Someone "kindly" pointed out a "mistake" in someone's message, which led to arguments about the usage of this terminology, with people quoting dictionaries (both online and printed) and using Google search result statistics to prove their point.
I once heard a quotation attributed to Samuel Johnson (which I haven't been able to find online): "I never correct anyone's English. If he is my equal, it is offensive, and if not, it is patronizing" (or words to that effect). I agree with this sentiment, and try not to correct people's language unless they ask me to.
In both the cases described above, people seemed to be driven by the desire to appear right in public, without considering the impact of their remarks upon others. It seems to me a very competitive attitude. If I really thought it was worth correcting or questioning something a person wrote to a list, I would probably do this in private. Then the list member could, if necessary, correct the public message accordingly, without having the public embarrassment that resulted in these cases.
When I consider my actions, I am driven more by wanting to do the right thing than by wanting to be right, at least in public. I am confident enough in my knowledge that I don't need to show off or say "I know better than you", and considerate enough to think about how other people would feel about what I write.