Macedonians, like other Greek city states and kingdoms, decided that resisting the Persians is futile, so they succumbed without battle. Like Denmark in WWII
Also it was Philip who dreamed of the Greeks invading Persia as a revenge. Greeks. Not Macedonians or Athenians -who had suffered most that any other city states.
Mythology some times give some useful info, in that occasion mythology doesn't say anything about titans or cyclopes or gods, it says about Greek settlers who built their kingdom in an area later called Macedonia.
"Alexander (son) of Philip, and the Greeks apart from the Lacedaemonians", as the epigram goes
The Spartans would never agree to be part of a campaign which did not have them as the leader.
Btw, Thessaly and Boiotia did not fight the Persians either in their invasions, would that make them non-greek too?