Fair enough. Sounds like A is going to have to decide whether they talk to B directly, complain to the supervisor that B still isn't meeting expectations, or drop it. But keeping you in the middle isn't going to solve the problem and it needs to stop. You can say that firmly but nicely and with validation. (The validation is important to maintaining your relationship with A.)
At the end of the day, this sounds like a failure at the management level. If B is known to be underperforming, it's on management to either find a way to help B improve or replace B. Management's failure here is hurting all 3 of you. A has a right to be pissed. B needs guidance or the boot. And you need to be free of this mess.
I used to feel the same as you. But the short answer here is because the law chooses to focus on the welfare of the child over either of the parents. It isn't about being fair to the mother or the father. The mother and the father made the child. The child needs care. The mother and the father are the most reasonably responsible for its care.