Correct moral behavior requires following objective standards, not personal whims and passions. Only God can provide such objective standards.
How can we adopt a moral system without there being a God? If God does not exist, is there any basis for ever being moral? That's the fundamental issue when discussing atheistic and theistic morality not whether atheistic morality exists at all but instead whether any atheistic morality can reasonably be adopted. Thus some religious theists argue that only the existence of objective standards which we are required to obey provide a secure basis for morality and moral behavior.
This question can actually be rephrased on a more fundamental level, usually referred to as "metaethics." People who espouse this myth usually subscribe to a metaethical perspective known as deontological ethics. In deontological systems, being morally good is defined as obeying certain moral rules. When you follow those rules and do your duty, then you are good regardless of any other considerations like whether the consequences of that obedience lead to suffering or happiness. On the other hand, if you ignore or break any of those rules then you are not doing your duty and are morally bad once again, regardless of any consequences.
If you assume that the only possible moral system that can exist is deontological in nature, we have to ask where those rules and where that duty can come from. If there is a God, the answer will seem obvious, but if there is no God, there wouldn't seem to be a source. If there is no source for the rules to obey (and, by extension, no eternal rewards or punishments for those who obey or disobey), then there would be no reason to obey any rules that might come along.
Given such premises, it will seem reasonable to conclude that if there is no God, then there is no reason to be moral. Must we, however, accept those premises? No. The premises are not unusual, but they are also not unassailable. There is no reason why we should assume that the only justified moral system which can exist is one which is based upon obedience to a set of absolute rules which we must accept as a matter of duty.
There are other metaethical perspectives which are at least as valid at a deontological one, with the two principle ones being virtue ethics and consequentialist ethics. A person might have good reasons for rejecting them and preferring deontological ethics, but even if that were the case it cannot demonstrate the need for belief in any gods. There are valid deontological systems of ethics which are atheistic in nature, lacking any gods to provide a foundation for the rules being obeyed.
Many prefer a deontological morality because in a deontological system, the reason for being moral is generally assumed to be objective and imposed from the outside that's why being moral "matters." More than that, however, the question of why it should "matter" suggests some set of ultimate "reasons" that, presumably, only a deity can provide. This would be consistent with similar questions asked by many theists: why should love matter? Why should happiness matter? Why should anything at all matter if there isn't a God and a heaven?
The answers to all such questions are fairly similar. First, it need not be accepted that for anything to "matter," then there must be some outside force or entity to make it "matter." Second, it should be argued that if something is going to "matter," this can only occur in the context of some set of values we have. When we value a hot meal, having a hot meal "matters" to us regardless of any gods or spirits, or anything else. A hot meal may seem like a trivial example, but the same basic principle holds true for other things of much greater import as well and the reason is that the very concept of "it matters" is dependent upon what we do and do not value on a very basic level.
Why should getting along matter? It matters if you value your own happiness and the happiness of others. The question is, do you really need some being (like a god) to require that you take the happiness of others into consideration? Do you need to be told to be kind to others? Are you only capable of caring about others when you are obeying orders to care about others and are threatened with punishment if you don't but promised with rewards if you do? If so, then perhaps you do need to believe in a god in order to be moral and for morality to "matter" and you really do need a god in order to be moral. I'm not sure that I would necessarily call that "morality," though.
Why is it an inferior form of morality? First, there is no real moral merit in following an order anyone can follow an order while not all orders should be followed. Second, the ability to follow an order is more characteristic of robots and automatons, not free ethical individuals. If a person is to be lauded for their behavior, it should be because they choose the right path, not because they simply followed instructions correctly. Finally, a morality such as this can be the most arbitrary that exists. Decisions are completely separated from their consequences for others and the impact upon one's personality. Orders are followed simply because they are given not because they reduce suffering, not because they increase happiness, and not because they are in any way virtuous.