For users to progress with badges they have to criticise. Is there a worry that if the badge is earned by criticising someone with little background in the subject will put them off asking questions? Should the "critic" step be removed?
There seems to be two ideas behind the badges -- introduce people to concepts/tools/features of the site, and encourage people to do things that are needed but may be tedious. The Critic badge you refer to is the former, while badges encouraging X number of edits is the latter.
Downvotes are essential for the health of the website. It is how we distinguish between good and correct answers and bad, incorrect answers. There is no mechanism other than downvoting to establish if an answer is factually accurate. Comments could be left, but they are temporary. Flags are not supposed to be used for wrong answers and so they won't get deleted unless the original poster does so.
This leaves downvotes.
The badge does not say "Cast downvotes out of spite on a new user." Like all voting decisions, it leaves it up to each person to vote how they see fit. And that's a good thing. Hopefully somebody is using their downvote wisely and is contributing to the health of the site. If not, well, these things happen.
So like all of the badges, downvotes earn a badge because it is an essential feature of the site and can be tedious to go through and study questions and answers for their correctness and then vote accordingly. But it needs to be done, or the site dies off.