Nothing you did was wrong. You tried your best to work with a difficult person who tried your patience beyond acceptable levels. He is the person who has a problem interacting with other people more than you do, I think.

How much longer until the class is finished? You may be stuck with him for a few weeks. If he chooses to not participate as a team member you cannot force him to do so. You may end up doing most of the work but hopefully this will be over soon and I hope you can avoid him in the future.