I'm going to pick a movie that I know my son won't like.
Why would you choose a movie you know he won't like?
He's a big critic of movies and I'm having such a hard time doing things that is meaningful with him.
It's understandable that you want to spend time with him, but you're not sure how to do so in a meaningful way. You should not do something that is intentionally going to make someone uncomfortable. Instead, talk to him about things he likes to do, then you'll find out what you can do together.
I think it's good for him to be exposed to things that he dislike. He knows that he has a problem about movies and that solves the problem for me.
I don't think it does though, It sounds like you have a hard time connecting and picking something he dislikes is only going to further that. If you really want to bond, find something you both enjoy.