I'd like to take a moment to say that downvoting is not inherently bad. Both upvoting and downvoting have played a very important role in the day-to-day operations of the site.
While there are many reasons a user might downvote a question/answer, the thread binding them all together is that the user does not like an aspect of that question/answer. Perhaps it is technically incorrect, or unjustified, or shows no effort, etc. Regardless of the actual reason, the downvoter found something wrong enough with the post to downvote it as a sign to the community that there is something wrong.
But a downvote alone does not fix the problem. Downvoters should let the OP of the downvoted question/answer know how his or her post should be improved. Usually, this is done with comments. And in this way, downvotes aren't usually anonymous (at least, not some).
I should also mention that it might not be necessary for every user who identifies a particular question/answer as wrong to downvote that question/answer. Piling on downvotes can be incredibly discouraging, and can get away from their purpose, which is to increase the quality of the site and help others learn math.
With all that said, I see no reason why a user can't ask what was wrong with their post, causing a downvote. The goal of this action is to learn what's wrong and correspondingly fix it. But to go after the downvoters aggressively is poor and, in my opinion, unacceptable.