Morality is both taught and also innate. But from what?
As a result, morality is a huge conundrum for the atheist. Morality for the atheist does not really exist, other than societal norms created over time that are based maybe upon nothing other than a mutual code of ethics to help society thrive. So, as long as you can get away with "bad behavior", so be it. There is no one watching and who then really cares?
But then there is still the guilt factor. You know if you have done something "wrong", even though "wrong" does not technically exist outside of a theology class. But then it eats at a person, which I think causes many psychological problems. And if you bypass this guilt long enough, you stop feeling the guilt. The Bible calls this searing one's conscience and the world calls it becoming a sociopath.
I have seen the wisdom of the morality of my faith to know that adhering to it's tenants has my best interest at heart, even though it may not seem like it at times. But as Paul even said at one point, if there was no resurrection all is vanity because our lives are but a vapor and unless there is a life after, it all is pretty pointless. Or go to the OT in Ecclesiastes where Solomon, who was the wisest of men, came to the same sort of conclusions.
Therefore, trying to divorce morality from God is nonsensical.