No one has addressed the existence of Moral Law. This desire to do good - even when no reward is offered - where did it come from?
And I'm never done being stunned at the response of people on this forum to religion (yes, I can understand bitter antipathy and resentful suspicion towards any form of religion), but seriously?
This has the effect of devaluing one's life. Most commonly, it results in wasted time and inhibitions that should not have been there. Sometimes it means going to war. Other times, it means accepting hardships (up to and including death) for one's religion (including doctrinal issues and to spread the religion). Rarely, people even kill their families and/or themselves hoping to take a shortcut to that reward.
Without religion, you are going to have good people doing good things. You are going to have bad people doing bad things. But, once you start adding religion to the mix, you start having otherwise good people doing bad things.