That only makes sense in case of "me too" comments. You have 4 options of response to somebodies comment:
1. Agreeing while providing some new information. So you write a comment (actually you'll probably upvote in this case as well, but whatever).
2. Agreeing without providing any new information. Like, "yeah it's completely right what this guy just wrote". That comment wouldn't be very useful indeed, so that's why upvoting exists. And that's totally normal option, because it's very much possible that some guy just "nailed it" and thus you don't have much to add, yet you want to show your approvement somehow.
3. Disagreeing providing new information. Like, "no, your statement is false, because that and that, here you have logical mistake and there you just got facts messed up: here some link for you to verify that". Obviously, that would be a comment. And that's what constructive conversation is made of.
4. Disagreeing without providing any new information, so you have downvo… but hey, wait, what was that? You can agree without providing any new information, but disagreement is meant to have some reasons for it. So if I disagree I'd better clarify why I disagree or just remain silent completely. Basically downvoting here just means "I don't like your comment" and it's quite reasonable that one shouldn't be able to do that unless he has something more to say. There's just no sense in such a thing as "disagreeing without explanation", unless that guy you disagree with isn't an obvious troll, and, honestly, you can never know if somebody is "an obvious troll" — it's quite likely that you just don't understand his reasoning, so if you don't want to continue discussion you'd better just ignore him.
Sometimes I disagree and someone else has already provided the new information I was planning to.
Sometimes I have a problem more with tone than with content -- someone was right, but being a jerk. I'll both downvote them and upvote someone else who was right and more appropriately civil.
Sometimes a comment is simply pointless. Someone posted a meme, a lame joke, or a comment that has nothing to do with the topic at hand (like "this" or "totally correct"). Downvoting is a nice shorthand for "this comment doesn't add anything to the discussion".
It's the distinction between "this isn't the content I'd prefer to see at HN" and "this comment is abusive or inappropriate for the venue". Karma doesn't mean much, and getting the occasional off-topic or vacuous comment downvoted is just a soft form of negative reinforcement.
In the first case, then simply upvote the comment you agree with. Remember that when you downvote a comment, you're essentially downvoting the entire discussion associated with that comment as well, affecting its visibility to others. Don't downvote substantive comments just because you disagree with them, it robs HN of quality content.
If everyone downvotes to disagree, the net effect is to reinforce the majority view and create an echo chamber. Use the downvote to enforce community standards, not community opinion. Many people have a hard time understanding the distinction, but it's an important one.
1. Agreeing while providing some new information. So you write a comment (actually you'll probably upvote in this case as well, but whatever).
2. Agreeing without providing any new information. Like, "yeah it's completely right what this guy just wrote". That comment wouldn't be very useful indeed, so that's why upvoting exists. And that's totally normal option, because it's very much possible that some guy just "nailed it" and thus you don't have much to add, yet you want to show your approvement somehow.
3. Disagreeing providing new information. Like, "no, your statement is false, because that and that, here you have logical mistake and there you just got facts messed up: here some link for you to verify that". Obviously, that would be a comment. And that's what constructive conversation is made of.
4. Disagreeing without providing any new information, so you have downvo… but hey, wait, what was that? You can agree without providing any new information, but disagreement is meant to have some reasons for it. So if I disagree I'd better clarify why I disagree or just remain silent completely. Basically downvoting here just means "I don't like your comment" and it's quite reasonable that one shouldn't be able to do that unless he has something more to say. There's just no sense in such a thing as "disagreeing without explanation", unless that guy you disagree with isn't an obvious troll, and, honestly, you can never know if somebody is "an obvious troll" — it's quite likely that you just don't understand his reasoning, so if you don't want to continue discussion you'd better just ignore him.