This is a difficult question to answer, because Greek history spans for so long. In light of this, I will make a number of points that may help you gain a broader perspective.
First, instead of thinking that the Greek used so many mercenaries, the truth of the matter is that the Greeks were often used as mercenaries. They developed a military formation called the phalanx and they were excellent infantry men. So, they were employed often in Persia.
Second, the Greeks did also employ mercenaries, but not excessively. The major Greek cities in the ancient world prided themselves on a citizen army. When they did hire mercenaries (such as from Thrace or Crete), it was due to several reasons. First, because there were incessant wars, more men were needed. Second, they needed a competitive edge at times, again due to the constant nature of war.