I've already casted 2 downvotes and I'm still not earning Critic: "First down vote". Hope this will help:
There are 2 downvotes cast already for my votes cast. What's wrong with the system?
Is this a bug or something that I have to wait?
It just takes some time for a badge-awarding task to run. There are tasks for various badges running at different intervals; some badges are more computationally expensive to verify than others. Critic is pretty easy, but still not instantaneous.