Why'd the Greek invent the concept anyway? Weren't they the Kings of philosophy? Why'd they wanna share the wealth?

Solon and Kleisthenes, considered the fathers of Athenian democracy (Athens being the first democracy we know of,) were both given power to institute periods of fierce rivalry between aristocratic clans and the various social classes - the poor often revolted against the rich at this time, when through debt they were reduced to the status of serfs or slaves. Ancient Greece wasn't like later periods in history; you couldn't terrorize people into obeying unjust laws with a couple of armed men. (Well, Sparta did, but that's because they devoted every waking minute to becoming the greatest warriors of the classical world. And they still had to put down several revolts.)

It is hypothesized that the goal of Athenian democracy was to diminish power struggles among families, making men beholden to the city-state itself instead of looking out for their own clan alone, as well as to give the less affluent enough of a voice in society to keep them content.