The best picks out of lane to counter Anivia include Jinx, Draven, and Aphelios. These champions are all great at countering Anivia with high win rates over 57%. Even if these Anivia counter picks are not chosen opposite your position, it's not a good idea to choose her into any of these matchups. They will likely win against Anivia.
Yet, if the other team picks either Zyra or Karthus, Anivia mains should strongly consider choosing her, as she easily destroys these selections with win rates over 53% against both ofthem.