This is pithy but brittle and I believe ultimately wrong. For example, if I wrong someone I hate, and then with a gun to my head I am forced to apologize when I wouldn't otherwise, I am not being moral.
One of the worst parts of humanity is that we're too often worse to those we are close to than to strangers.
I’d argue the opposite:
One of the worst parts of humanity is that we’re bad to those close to us in the name of far away, nebulous benefits.