In Death of a Salesman, when he's with Charley, Willy frequently insults him. Why would he do this to the man who is considered his best friend?

Willy's arrogance is an important element of his character. Pride is a part of the explanation for Willy's ultimate demise as he either will not or cannot recognize his moderate successes as anything but failures that fall short of his dreams of becoming a "great man". 

Willy's criticisms and insults aimed at Charley are an expression of this pride. Being competitive in his pride, Willy cannot concede that Charley is his equal (though he painfully accepts the idea that Charley is his superior at times). Pride and resentment are twin character traits in Willy, as they are in many actual people. 

Wishing he was better than he is, Willy strikes out at the man who reminds him of how far short he has fallen from the mark of his proud ambitions, for himself and for Biff. Charley has succeeded where Willy has failed, not through talent and not through "personal greatness", but through honest and hard work. Even Charley's generosity is a goad to Willy and a reminder of how poor Willy's decisions have been.

Charley exclaims, "You been jealous of me all your life, you damned fool!"

Willy insults Charley out of a childish need to hurt as he has been hurt, to diminish Charley as he feels he has been diminished. Resentment, jealousy and injured pride press Willy to this end.