Final answer:
The Greek City-States rebelled against Alexander the Great due to a historical value of independence and resentment of Macedonian control. Darius bribed and encouraged rebellion to exploit this sentiment and create political fracture.
Step-by-step explanation:
The Greek City-States were eager to rebel against Alexander the Great's rule primarily due to resentment of Macedonian hegemony and their cherished independence. Despite Alexander's prowess and his crusade being portrayed as a pan-Hellenic mission, many Greek poleis were perturbed by the loss of autonomy and their forced alignment under another's rule.
The historical context shows that the Greek City-States had a long tradition of valuing their independence, as well as a history of enmity with the Persians. The Athenian support to the Ionian revolt against Persia eventually led to the Persian wars, and the subsequent creation of defensive leagues aimed at resisting aggression illustrates their desire to remain autonomous.
Furthermore, the Hellenistic Era under Alexander saw the spread of Greek culture and influence, but the political dynamics were altered as local dynasties were replaced by Macedonian rulers, some adopting similar governance styles as Alexander himself, offering alliances and rich rewards to those who accepted Macedonian rule. This could explain the willingness of some Greek poleis to accept bribes from Darius and rebel against Alexander, as they sought to regain their former independence or negotiate better positions for themselves under a new regime.
Notably, after the death of Darius III and Alexander's victories, the consolidation of Greek and Macedonian rule in the former Persian territories was not solely a result of military conquest but also of strategic administration and the establishment of new trade routes and cities by the Hellenistic monarchs.