One could argue that an upvote is more often about agreement than a downvote is about disagreement.
However that norm changed when people realized that was a bad idea.
The UI didn't change with the norm change.
At one point the norm was you could downvote to disagree if the comment had a score greater than 1. But now that comment scores are no longer displayed, that norm changed too.
Now the downarrow basically means spam/stupid/useless, etc. Actually for spam you also need to click on flag.
The reasons for clicking may not be symmetrical, but the actions when clicking are symmetrical. The points go down with the down arrow and the points go up with the up arrow. This is symmetry even if the reason (agree, disagree, quality, spam, etc.) for the increase and decline of the points is asymmetrical.