What the reality of the situation is, was that ancient Greeks were a very splintered group of people, that worshiped similar gods and goddesses. The Spartans, strong and brave, were the muscle of the land of Greece. While the Athenians were the mind and heart of the nation, where the strong minded and philosopher called home. You'd think they would get along, worshiping the same gods and all, but that would be farthest from the truth. These two nations went to war, they call it the Peloponnesian War, it devastated Athens and changed the balance of power in Greece and Persia.
Athens was, as I've said, the home of knowledge in the ancient world, the city was responsible for all three great philosophers; Socrates, Plato, and Aristotle. It was also the pinnacle of Art as well, detailed bronze statues were recovered from the Mediterranean and show a level of precision not even a computer could match today.(Though I don't think so.) Their architecture shows a great knowledge of mathematics, being the first to build a crude elevator to move stones. The Athenians worshiped the god Athena centrally. Athena was the god of philosophy and wisdom, she has an owl with her which is her attendant. The owl was depicted as a robot in the 1981 film Clash of the Titans, another classic example of: getting it wrong. The Socratic method was pioneered by Socrates in the city, and later was to be executed for "corrupting the youth". Athens sees itself as the last outpost for high culture, and sees Sparta as a barbaric tribe of militants. Problems arise.
Sparta was the southernmost Greek city-state, it's focus was military training, international affairs, and propaganda towards pushing that military unto their international affairs. It saw itself as the muscle of Greece, and it very much was. Starting their training at seven years of age, assuming they made it that far, they were taken away from their mothers and put in a platoon of boys. These boys would learn to die for each other, die for loyalty, and die for honor. Honor is the key word here, teaching them that dieing for the cause of Sparta was the way to live forever, was common practice. They saw the Athenians as their rivals and strove to out perform them at every turn. Spartans developed a congress at which they would decide who their allies were and what the would do, for Sparta. The congress would be held in Corinth and was led by Sparta. Spartans actually befriended the Persians in order to defeat the Athenians during the Peloponnesian War, probably at one of these congresses. So, the Spartans weren't all that barbaric, they created a congress. Even though it was for the sole propose of starting war, it still speaks volumes.