My husband could not sing in tune, but could tell when an instrument or another voice was out of tune. We eventually worked out that when he tryed to sing he mostly listened to himself, not through the air, but through the bones of his head, and they were "out of tune".
By doing the classic folkie, cupping his hand round his ear, he created a stronged passage for sound through air and could hear himself properly, and so learned to siong in tune, but it always felt to him, as if he were singing flat.