Upvoting shows support for someone else's argument, which is what you do if you agree with someone and don't have anything else to add. It's a compliment. That's ok.

Downvoting can be okay, but I actually think it's a bad feature, as it just leads to hate. But if someone is spamming, or someone is abusing features of the site, I guess it might be alright, if used with discretion.

Excessive downvoting is a form of the ad hominem fallacy, as you are trying to discredit the person by lowering the credibility of what they have said. It is offensive, hurtful, and also extremely childish.

Why do people constantly do things they claim not to care about?

The identity of the voter should be displayed in all cases. Down voting is the cyber equivalent of nasty anonymous poison pen letters. The act of a cowardly sneak.

Well, I don't really care about the upvoting and downvoting, but some people do care. I would say that if one was to vote an argument up, or down, they would need some sort of reason. I don't think most people enjoy seeing poor arguments upvoted and well written arguments downvoted.

It's often nice when you can think of an argument and rather than write a new post about it just like a similar post, like a vote for your opinion. Also it lets the person you vote up or down feel either supported or unsupported to let them know the popularity if their argument, which on a debating site in particular can be useful. I do agree though that it fuels hate

I take it as a sign that other CD'ers either agree/disagree with my opinion, or believe I made a logical point (or not).

It makes more sense than the Allies, Enemies, and Hostiles functionality. I disagree with some people here fairly consistently, but still, why make them an Enemy? I might agree with that person on the next debate.

Well these options enable the weekly leaders to get on top of each other,there's no harm in down voting some comments so long as you're not doing it frequently.As for the other,up vote yourself and gather a virtual point