I question the idea that ant-vaxxers believe that more people will die from the vaccines than COVID if no one takes it. I’ve never heard an anti-vaxxer explicitly state that and they always shy away from direct questions like “Don’t you think that the benefits of the vaccine outweigh the possible side effects?”
I think they are mostly just afraid and are letting their personal feelings get in the way of seichel and common sense. They don’t want to take the vaccine, so they justify it with mounds of contradictory and vague statements.