i don't see what's wrong with downvoting on disagreement. does it hurt people's feelings?
And that's OK, for truly unwanted behavior.
But the right kind of disagreement is good, healthy, necessary and should be celebrated.
One option would be to have two axes of single-click vote-reaction. One is classic up-down promote/demote, for whether a comment has quality. The other would be left-right agree/disagree, a mini poll to capture sentiments.
Unless there is an easy outlet -- a click-region -- for sending a 'disagree' signal separate from the 'disapprove' downvote, it is inevitable the two will be conflated, causing angst and periodic threads like this one.
For previous discussion on this 'two-axis' concept, see: