Morality arguments are social and contextual. That 2+2 is 4 won’t change and captures some sort of eternal truth while what is deemed moral is constantly changing over time and differs across different societies and social groupings.
So morality arguments require and appeal to a particular shared sense of right and wrong. If Chomsky was guilty of sexually abusing children, then I do not share his moral foundation and so his appeals to morality arguments do not convince me.