I totally agree with this (they are using this as an excuse, perhaps, to make you move?), but it's probably best to move...mold isn't good for you or your pets anyway.
All depends what your lease agreement says as far as what is legal for them to hold you accountable for. Read it carefully, if you didn't before...& get help if
you think you're being taken advantage of...yours wouldn't be the first landlords to try it. Been many many years since I've rented, but I've fought a landlord
& won when they tried to keep my deposits to cover their losses from other tenants (they later admitted that to me). I'll admit that I fought a little dirty thoughI told them if they didn't refund my deposit I was going to let some total dirtbags move in (in my place) & then they deal with evicting them. They
didn't like that idea at all & I got a prompt payment of money they owed me. (You do have to look as though you mean what you say, I guess I fooled them?)
I'd also be asking what's on the other side of the walls of the room where the mold is...are you on a top floor apt? Probably a roof leak that is coming down
inside the walls, but could also be a plumbing leak causing the moisture.