Carmine Lupertazzi's son, Little Carmine, obviously isn't all that bright a guy. In fact, didn't Junior refer to him in an earlier episode as "Brainless the Second"? He has more ego than smarts, it seems.

When Carmine Sr says that he would've been proud to call Tony a son, Carmine Jr's emotions of shame (his father obviously is disappointed in him) got the better of him, and he forgot about business. Instead of concentrating on business (which would've been smoothing things over between the New York Family and the North Jersey Family), Carmine Jr tried to verbally cut Tony down, which furthered the rift between Tony and Carmine.