It seems that he sees you as in charge. He sees it as your responsibility to decide who does what and to ask him to do X if you decide you want him to do X.

So you must ask him, but you don't like to ask and if you ask "too much" you are nagging.

So it seems that everything is on you: to decide, to ask, but not to ask "too much".

It sounds like you are not intrigued or engaged by the task of drawing him out.

I wonder if responsibilities could be divided in an adult manner. For example, maybe it could be his responsible to (say) do the dishes every night, period. That would be one of his jobs, he is expected to do it, and he is in the wrong if he doesn't do it faithfully, every day, period, without being asked.