As far as I've always understood it, upvotes and downvotes relate to the value the voter perceives in an item (article or comment). If you think that the item adds value, you'll upvote it.

In most cases, agreeing with something is a prerequisite for seeing it as adding value. As a consequence, since people mostly upvote what they agree with, one tends to equate upvoting with agreement and downvoting with disagreement.

However, according to my understanding, downvoting should be used when you think that the item adds no value (or adds "negative value"). This is not the same thing as disagreement. Some examples of items that either add no or too little value are: name-calling, snarky one-liners with no useful content at all and very badly edited text (maybe the content has value, but the form negates it).