Originally Posted by Ludens
I think it may have been a combination of social and military issues that prevented Greeks from establishing effective cavalry. As pointed out earlier they lacked an equestrian tradition and good horses. For a long time they didn't have any extensive military training either. The resulting cavalry could not do hammer-and-anvil tactics. They were simply too weak and too little trained to perform a shock charge, and a hammer is no use if it does not hit hard. Also, early hoplites were far more mobile than phalangilites, and as such would have found it little trouble to turn and face the cavalry. As such, Greek cavalry mainly were scouts and skirmishers.
Also, the Greeks idealized the hoplite and his bravery and steadfastness in battle. The fluid hit-and-run tactics of skirmishers were looked down upon as cowardly. Given that Greek cavalry was mainly used for skirmishing as well, I don't think they were held in high regard. This is off course not conductive towards developing more effective cavalry.
It is easy to say that the Greeks and Romans should have developed better cavalry, but in the end of the day it is a hell of a job to get good horsemen and good horses trained, and very expensive to boot. It also requires an institution (e.g. the army) that organizes this. The Romans and Greek simply did not do things this way. They just called their citizens and allies, and these turned up with whatever equipment they had. As such, they couldn't train their citizens to become better horsemen. And, when all is said and done, they seem to have done fairly well without it.