The difference between an argument and a debate is that a debate is not personal, it is only an idea or opinion that could be changed given enough evidence to the contrary. An argument is on a personal level and when some disagrees with your personal belief system and you take offence and fight back, you are not willing to change your opinion.
A debate should be an educational experience for both people involved, sharing their ideas with each other with a common goal of further understanding, but when you try to force your ideals on the other party it can turn nasty.
What's worse is when you or the other person can't let it go after the conversation is over, and then you research your information to find proof of your opinion for the sole purpose of proving the other person wrong, thus making you right.
Some people need to feed their ego, they cannot stand being wrong, and they will go out of their way to prove themselves right even though it can harm their relationship.
Some people don't seem to understand that after a conversation is over, it should stay that way, especially if it ended badly, and no good can come from bringing up the topic again, and this holds especially true, if the only reason that you are bringing it up again, is to prove to the other person, that you were right and they were wrong.
Sometimes you do need to revisit a conversation, to repair the damage done by it and to come to common ground with each other. The topic in question will keep coming up throughout your relationship and it needs to be addressed, but only for the purpose of solving the problem between both parties, and not from malice or for the need to Prove Someone Wrong, To Make Yourself Right.
Scott Goerz