Well, the good news is that you take responsibility for your part in it. There there are always situations where emotions can get out of control and nobody seems to be able to back down. It happens to everyone and even when it's something that seems dumb it's probably not just that one thing, kwim?

Since you asked for suggestions, the way I usually look at things like that postmortem is to analyze whether I seemed to be the one baiting the other person or whether they were baiting me more. It doesn't really matter who's pushing the argument to greater heights but it can be helpful to analyze your part in it for future reference. If you didn't like it and you can figure out what went wrong you can make sure it doesn't happen again. Did you feel like arguing or did you get sucked into it? It can also give you a basis to figure out if you need to be the one to apologize.