I'm reminded of what a rather self-aware pwBPD I know of has said:
"I'm crazy, I'm not stupid."
The point being that all of these flaws he has, the ways he's dropping the ball, avoiding doing work he is asked to do, etc... .he's not so stupid he has zero clue that he's doing anything wrong. No, he's crazy. His emotions are overwhelming him and making it so he cannot do the (apparently simple and easy) things he knows he should be doing and needs to do. And he spirals deeper into self-hatred and blaming, then cannot take that, so he projects it onto you and turns it into a fight, because it is easier for him to deal with fighting with you than it is to deal with accepting that he let you and himself down... .again... .
Consequently, explaining what he did wrong or holding him accountable for it will just make things worse, not better. All it does is point him back at the self-hatred, etc... .
I asked him to email a response to a monthly very important client since I was doing all the physical job. He did not.
And here is where you have to figure out how to walk a subtle line as a business partner. Perhaps you should have emailed the response instead of expecting him to do it. If you had, it could have been one of either two things:
Are you enabling him to be irresponsible and drop the ball, by picking it up and dealing with it, and protecting him from the consequences of his behavior?
Are you doing the part of the business work that he is incapable of doing well? (Perhaps asking him to email a client even though you had done the part of that job that he 'normally' does was a bad idea in the first place?)