Q: Can atheists be good?
A: Yes: indeed many self defined atheists are more moral than many Christians – in terms of their patience, common sense and generosity. To be human is to have the imprint of the moral law on us.
Q: Can atheists explain the origins of morality ?
A: That is a different matter all together! The short answer is no. Atheists could arguably explain the evolution of moral behaviour and feelings: perhaps it was necessary to have the illusion of morality for the propagation of stable social groups. Maybe feeling “as if” there are moral rules gave some evolutionary advantage.
Now, if evolution blindly gave us moral feelings, or if human society invented moral rules, then I can ignore them when it suits me. That would be perfectly rational – the universe doesn’t “care” if I’m immoral. But morality is all about “oughts” - things that I must do, that have a necessary call on my behaviour. There are moral laws and to explain moral laws you must have a law giver.