The Delian League broke up because when when the Athenians turned the "Delian League" into what amounted to an Athenian empire (by asserting the control over cities in the league), the Spartans reciprocated by forming a "Peloponnesian League."
The Delian League broke apart after it became an Athenian tyranny, which was defeated by the Peloponnesian League.
Explanation:
The Delian League was a military alliance of polis of ancient Greece to defend themselves from the Persians. It was organized around Athens and included the Ionian cities of Asia Minor, Calcidia, Euboea and the Cyclades. Each polis had to bring ships and soldiers, and his treasure was kept in the sanctuary of Delos, in Athens. However, Athens appropriated the treasure and, as a hegemonic polis, forced the rest of the polis to pay him a tribute. Upon the outbreak of the Peloponnesian war (431 BC to 404 BC), Sparta appeared as the liberator of the cities of the league. The Spartan victory was the end of the league.
