It's true that "full human rights" is a relatively new concept. That is - the concept that any competent adult has the right to vote and the same basic legal protection as the richest people in the land is relatively recent.
After all, it wasn't until the early 20th century that adult women were considered competent enough to vote. Even the U.S. Founding Fathers really only trusted the state legislators to appoint the U.S. Senator (the direct vote was only fully implemented in 1913 when the 17th Amendment was ratified).
But how did this evolution begin? The British Library starts the process in 1215 with the Magna Carta. This is pretty much what I was taught in my high school civics class as well (although it's crushing to realize the Magna Carta is really guaranteeing the rights of a bunch of angry barons and really says nothing about the general populace).
Does this mean that there was no concept of human rights before 1215? Although our popular notions may date human rights to 1215, the issue has been present for large portions of Western history. Peasant revolts were quite common in the Roman Empire, so the lower classes certainly felt they were owed something more. In fact the Roman government created the office of tribune specifically to mediate disputes between the plebes and the patricians (the aristocracy). The basis of Athenian democracy (and the Roman Senate of the Republic) was to allow "eligible citizens" full participation. Both the Ancient Athenians and the Roman Republic rejected the notion of an absolute monarchy - this is the concept echoed in the Magna Carta. On a side note, Athenian democracy was innovative in allowing any adult non-slave male to vote in the city assembly. In Rome, only designated patricians could participate in the Senate.
In the British Isles, the concept of civil rights was also found in both Anglo-Saxon England and Celtic Wales and Ireland. Before the Norman invasion of 1066, the selection of the next Saxon king had to be ratified by the witengemot Assembly Similar elections were held for Welsh and Irish kings - although the candidate pool was usually pretty limited.
Finally in Irish law, the aristocracy were legally obligated to provide certain provisions to the peoples within their territories including feasts (some with ale, some without). Non-slaves were also guaranteed certain rights in terms of seeking redress, even from the ruling class.
So I would have to say that civil rights were a concept that had been around for a while. The interesting question is - why do we choose the Magna Carta as a starting point? It's pretty much an Anglo-centric quirk. England generally dates the start of English history to the Norman Invasion of 1066. Not only did this bring in a new dynasty from France, but a brand new aristocracy as well. The native Saxon male nobles were pretty much displaced and replaced with French imports, and all the major government institutions replaced.
Events before 1066 are "prehistory" (even if we have documents). The events of 1215 (less than 150 years after the Norman Conquest) is one the first events in the NORMAN ERA where civil rights were successfully asserted. Before that Norman king had much more power, even over his nobility.
Although I begin this blog with a complaint that the Magna Carta wasn't the beginning for Civil Rights, I realize that it actually is a milestone for the English aristocracy. The native Saxons, on the other, hand still had a fair bit to travel...although they did get there eventually. It is a little disconcerting to realize how much history can be written by the winners, even ones from nearly 1000 years ago.