Vizzini was a very arrogant person when it came to his intelligence. When Westley challenges him to a "battle of wits" he is entirely confident that he wil win. He taunts Westley and tries to convince him that no one could be smarter than himself. Before this point, Westley has defeated Inigo and Fezzik, but has not killed them. However, he kills Vizzini. The reader knows that Westley is very smart, and probably could have figured out a way to defeat Vizzini without killing him. One could argue that he killed Vizzini because he is the leader, but at this point Westley doesn't really know that. He only knows that Vizzini, Fezzik, and Inigo are on the same team. This leads me to believe that Westley killed Vizzini because of his merciless and arrogant personality. The other two had not wanted to kill Westley, and had been fairly polite before they battled him. Vizzini, however, wanted to kill both Westley and Buttercup, and was very arrogant about his ability to do so. It is likely that this angered Westley, so he killed Vizzini instead of simply defeating him. Overall, Vizzini did not behave appropriately, and his poor behavior ultimately led to his death.