Some things are harder for people.

From what you said, it does not sound like he is doing nothing at all. He isn't refusing to help, he just does not know what is expected of him. I have a hard time doing things unless I have a schedule. It's not that I don't feel responsible and you said he cooks, takes care of the child and cleans up the kitchen. Maybe when he lived alone he did not do these things and his house was messy. My room stayed that way for a long time once.

Just because someone is an adult does not mean everything is easy for them. If you and him make a schedule together that you both agree to he would know what he needs to do every day. You are not treating him like a child, you are treating him like someone who struggles with something and needs extra help.