Properly understood, the moral argument is one of the most effective arguments in Christian apologetics. As William Lane Craig says, this is because "it hits people where they live". Although the Lord reveals more to some people than to others, the Bible tells us "For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law (for not the hearers of the law are just in the sight of God, but the doers of the law will be justified; for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves their thoughts accusing or else excusing them) in the day when God will judge the secrets of men by Jesus Christ, according to my gospel." (Romans 2:12-16).
Because of this, everyone knows there are moral laws. Yet, moral legislation requires a moral legislator. Therefore, the moral argument is not so much an argument for God's existence, but an argument to show that, at least subconsciously, everyone already acts as if they know God exists. Everyone has a concept of right and wrong. Even a psychopath, lacking normal moral understandings, will at least seek justice when something is done against them (not to mention them being the exception that proves the rule).
But atheists might reply to this by suggesting that God is not necessary for morality to exist, as there are secular ways to establish moral systems identical to the ones we use today. The problem they have is that there is no such thing as a unified secular moral system. Atheists do not always agree on what is right and what is wrong.
This is because secular arguments for morality depend entirely on the intended goal. Obviously, it is possible to make a secular argument for living according to a set of moral beliefs. This is because God has set up a universe of cause and effect. The question is, what is the effect we ought to seek to cause? Because atheists do not agree on a specific goal, atheists will never agree on morality, no matter how many logical arguments they make for how to achieve their goals. Some atheists might believe that length of life is the most important goal. Others might believe that the preservation of our species as a whole is more important. Some might believe minimising suffering, or maximising pleasure is the goal. Do we treat all life as valuable, or are some lives more valuable than others?
Just watch Matt Dillahunty debate Alex "Cosmic Skeptic" O'Connor on the topic of veganism and tell me that these two people, however much they may reject the existence of God, are ever going to be able to agree on the morality of consuming animal products. It's never going to happen, because they value animal well being differently. O'Connor favours compassion towards animals, whereas Dillahunty, while he doesn't seem thrilled with the idea of abusing animals, he nevertheless tends more towards his own pleasure. In other words, atheists can never agree on the effect they wish to cause, and so they will never be able to argue for moral behaviours.
This is where the atheist will point out that Christians also differ on morality. And it's true, we do. Here's the difference: God never differs on moral issues. See, the Bible teaches us very clearly that all human beings are sinners. Christians do not convert and instantly become Jesus. Christianity is a never-ending war between our spirit, renewed by Christ, and our flesh, bound by the law of sin and death. This is not a war without casualties. Whether in ignorance, or even out of malice, Christians will disagree. But whereas atheists have no source that ought to unite them, Christians absolutely do.
Now, first off, there are two types of morality in Christianity. The first is law, the second is doubtful disputations. A doubtful disputation is a moral decision that is between man and God. Can I eat meat, or should I go vegan? Do I have to celebrate Christmas, or should I withdraw from all festivities? Can I get a tattoo, can I smoke, can I drink, is my hair length right, these are all trivial details that the Bible tells us we are not to divide over. Every single Christian in the world can come to different conclusions on the same issue, because God has given us permission to do so as long as they do not cross into legal territory. This is a case of genuine moral relativism. I prefer a vegetarian lifestyle, I can't force that on you. If you want to eat meat, you can't say I have to as well.
Law, by contrast, is something that is not so open ended. These are commands that are binding upon man, and although Christians do differ on these issues, there is really no excuse to. There are reasons we do. As I said, the first is ignorance. Christians do not share equal amounts of knowledge. The second is malice. Christians are still sinners (and of course there are wolves in sheep's clothing). As sinners, we still rebel against God, sometimes to the point of denying His commands. "Did God really say?" is the very question that caused our species to fall into sin in the first place, and allows us to continue trying to justify ourselves to this day. Furthermore, not everyone who says they are Christians actually are. The Bible even tells us it is possible to preach "another Jesus" (2 Corinthians 11:4).
Because of this, it is not fair to pit Christians against each other as if our disunity proves anything more than this: The Bible is right to tell us all have sinned and fallen short of the glory of God, and if we say we have no sin, we are lying, and the truth is not in us. It's like saying because I can never hit a bullseye, the dart board is badly constructed. The problem for atheists is they have no dart board. They are throwing darts at the wall, and when the dart happens to stick in the wall, they say "See! My method of throwing darts works!" Ok, well congratulations, you hit the wall, but those darts were not designed for walls.
But Jesus is the perfect dart player. There has never been a time when He fell short, every shot He makes hits the bullseye. That includes when He walked the Earth as a man. Born to the virgin Mary, Jesus lived the perfect moral life. Yet, though He never sinned, He was punished as a sinner. Not for His sin, but for ours. Every time we have differed morally from Him, He was punished for. Thus, we can be treated as if we had lived His perfect life. All it takes is faith. Confess Jesus as Lord, believe He was raised from the dead, and you will be raised with Him into eternal life.