Morality and atheism are obvious opposites. One is a set of laws by which humanity ought to abide, the other is a philosophy that rejects the existence of the legislative body that both writes those laws, and holds man accountable to them.
But of course, atheism does not automatically mean evil. The Bible, after all, makes it quite clear that even unbelievers have the law written on their hearts (Romans 2:12-16), meaning even these unbelievers usually possess a conscience. Atheists therefore face the problem of knowing moral laws exist, yet not being able to account for them.
Or are they? Not surprisingly, atheists do try to account for the morality they know exists without the God they claim doesn't. The problem is, all of these attempts fail. One such attempt is almost surprising, because despite the fact selfishness is almost universally seen as the opposite of morality, it is here almost explicitly used as the source of morality. Our own self-interest is used to say that morality makes perfect sense in an atheistic worldview.
Good morals, of course, are beneficial to us if everyone abides by them. If society agrees it is wrong to murder us, our chances of being murdered are significantly reduced. If we can agree to property rights and fair trade agreements, we end up working for each other. You use your talents and resources for me, and in turn I use mine for you. That works.
And indeed, it should work. A well-written law provides benefits and/or minimises drawbacks. As the perfect legislator, God's laws should work, even if an unbeliever is merely obeying them because they work, and not out of love for God.
The problem is, alternate morals can and do have similar outcomes for the individual. To illustrate this, let us consider a simple chicken. A chicken, just like us, looks out for its own self interest. No chicken wants to end up in some KFC boneless banquet, chickens want to live. And yet, because humans are the dominant species, we still eat them. Even if we don't eat them, we still steal and restrict their freedom so they produce eggs for us, along with other things you can use them for if you know how. The relationship between man and chickens is decidedly skewed in our favour.
As a Christian, I can cite the dominion mandate in favour of this. Mankind was given dominion over all the animals, and after the flood, was also permitted to eat all of them. Therefore, I can say it is morally acceptable to eat chickens. But for an atheist, there is no moral argument for how we ought to treat our fellow man that cannot equally apply to a chicken. If we're going by the self-interest standard, the same concept that allows us to dominate chickens for our own benefit would allow us to dominate our fellow man for our benefit. Obviously, eating them is out of the question due to the serious threat cannibalism poses to our health, but what about slavery? If we can dominate hens and force them to help with the gardening, why not also dominate weaker members of the human race and force them to do our bidding? We could even selectively breed them so that, over time, they become domesticated and well fit for slavery, almost as Charles Darwin predicted whites would do, only instead of exterminating the "savage races", we utilise them.
And so we see that selfish morality, far from being a source of objective morality, ultimately shows why we need objective morality. If our own self interest dictated the difference between right and wrong, we could use our own self interest to justify any number of atrocities.
Furthermore, as previously noted, selfishness is usually seen as the antithesis of morality. This is especially the case in Christianity, in which it is seen as more blessed to give than to receive (Acts 20:35). Exemplifying this is our Lord Jesus Christ, who was so selfless that though we deserve nothing but wrath for all of our immorality, He received that wrath upon Himself on the cross. Through faith in His resurrection, we can receive the reward due to Him for His righteousness. It is definitely in your own self interest to repent of your sin and follow Him.