I think arrogance is a part of wisdom which is foolish. As Shakespeare said: Better a witty fool than a foolish wit.
   

Once upon a time, a friend of Socrates asked god in the temple of Delphi that whether there are someone smarter than Socrates, but god gave a negative answer. The oracle bothers Socrates, and he visited many people whose mind full of knowledge. He finally reached the conclusion that since god never tells a lie, so the only correct interpretation of the oracle is that Socrates is one of the most intelligent person, because only he does not "knows nothing but pretends to know", but honestly admit his own ignorance. Socrates' cleverness is his ignorance that humility - hunger for infinite truth and honor. As a result, people should be themselves like Socrates, which looks foolish but that is wisdom and smart.
   

Foolish people often only know that they are smart, but they don't know they are stupid, they will not admit their shortcomings and errors. Every foolish people always have the ability to find at least one person who is more stupid than themselves to boast themselves. Because they feel they are always right, so they think they don't need to correct shortcomings and mistakes which means they are always wrong.