The correct answer is "the need for the islands to be protected from the Persians". This is because during the Greco-Persian Wars, the Persian Empire posed a threat to the Greek city-states, including the islands. The Persian Empire had a powerful navy and sought to expand its territory, which put the islands at risk of invasion and conquest. Therefore, it was necessary for the islands to seek protection and support from Athens, which emerged as a leading power in the Delian League, a defensive alliance against Persia.