Per Logic 101, your friend’s failure to live as though there were no right or wrong doesn’t disprove his assertion by itself (if we argued that, we’d be committing the tu quoque fallacy). But I would think raising this point might at least get him to reconsider his position.
Regarding JohnD’s comment above, a number of authors have pointed out the curious fact that all human societies throughout history have recognized certain things as right or wrong. In the West the notion of natural law is (in part) built on this observation. C.S. Lewis famously referred to this body of shared morality across cultures as the Tao in his book The Abolition of Man.