Just how could Persia lose to Greece?

As we know that horsed units such as cavalry played a significant role in the military culture of early Iranics, Achamenids were no exception but as we understood of the accounts of battles such as Guagamala as an example of the late Achaemenid, apart from the nature of a disorderly army composed of mercenaries, although cavalry were important, we see no brilliance as from the part of the cavalry. Comparing this with the quoted cavalry brilliance of the Parthians and Sassanids in many Roman accounts we can conclude that Achaemenids didn't pay heed to this matter like Parthians for instance. Another mysterious point is the defeat of the Darius I at hands of Scythians, this also to some extent shows that Scythians were superior in terms of employing cavalry and Achaemenids somehow receded from this old Iranian tradition of warmongering. (also considering the fact that one of the main reasons of their defeat was fighting in the enemy's ground far away from supplies and home). 

The importance of this is despite Macedo-Greek warfare development which was a substantial factor in defeating Achaemenids, Phalanx regiments actually faced major problems fighting Parni (Parthian) and Scythian cavalry especially their horse-archers, whose fighting style was more Iranian than Achaemenids, the thing which led in the overthrowing of the two Macedo-Greek Kingdoms in eatern lands of Alexander's empire (i.e. Seleucid empire and the powerful Greek Bactrian kingdom).