The moral argument is often counteracted by a number of subjective proposals for the source of morality. It's the government, or it's society, or maybe it's just every man for himself when it comes to morality. A common suggestion is that morality is determined by the amount of suffering it causes. If something causes suffering, it is evil, whereas if something reduces suffering, it is good.
We won't address the fact that this question assumes suffering is a bad thing. Let us instead roll with this assumption. Let's say that anything that causes suffering really is bad, and anything that reduces suffering is good. In this case, we should stop having children. Aside from causing pain to the mother during childbirth (not to mention the 9 month ordeal leading up to it), reproduction causes a brand new receptor of pain to come into existence.
By contrast, death, which is inevitable anyway, ends all suffering for the individual. Thus, while reproduction causes suffering both to an existing being and creates an entirely new being capable of suffering, it would be positively heroic to end all the world's suffering by just launching a nuclear war to obliterate all life on earth.
This is obviously not a viable option. No sane person would say that murder is a good thing (though unfortunately there is a growing number of insane people who are perfectly ok with killing the most innocent members of society). Thus, this principle cannot be applied consistently. You cannot say that pain is automatically evil and the reduction thereof is automatically good without justifying the destruction of the planet.
But there is a principle that can be applied consistently, and that is to put God back where He belongs. We don't need to try to explain the existence of morality without God because God actually does exist, and He is the source of all morality.
Unfortunately, we've all sinned against Him, and are thus worthy of His wrath. But in His mercy, He is not willing to execute it upon us (Ezekiel 18:32; 33:11; 2 Peter 3:9). Someone has to pay, but it doesn't have to be us. This is because God sent Jesus to take our punishment on our behalf. Through faith in His death, resurrection and Lordship, we can be forgiven for every time we have opposed God's morality, and inherit eternal life with Him.