>>2 I don't think it's childish to stop arguing with someone if it turns into name calling and gets really heated, however I agree that it is childish to simply block them. You have to settle it with them and make things right, instead of copping out.
Now, if he really was continuing to attack you after the discussion was done (and not in the minutes or hours afterwards) then blocking him is the right move. However, if both of you called the other a name or two, it doesn't make sense to block him just because of that.