The People of Athens and Sparta were arguing over who was better. But in reality an earthquake weakened Athens and Sparta grew stronger. They took land near Thebes and Corinith and they were able to unbalance their control and become allies with Sparta. They then started war in 431 B.C.
As you know war broke out in 431 B.C, would you like to know why? The allies of Sparta (Thebes and Corinth) to attack Athens that's when the war started. The war would push on till 404 B.C until Athens would surrender to Sparta.