The problem is there is no indication that religion makes people behave better. In fact, there is a reverse correlation between how religious a nation is and things like murder, rape, out-of-wedlock childbirth, etc. The U.S., which is one of most religious of the first-world nations, has the worst record on these things.
Some have suggested that religion may actually be the cause of bad behavior. It encourages people to focus on their duty to God rather than their duty to their fellow man. It encourages an attitude of "you made your bed, now sleep in it" toward people who make mistakes. It suggests that misfortune is the result of offense to God, and therefore needn't be remedied by human action. It also encourages people to gather into sects of like-minded people and fosters disrespect for people with different beliefs. It also discourages workable birth control in favor of unworkable abstinence programs, and then condemns and washes its hands of people who get pregnant.
The idea that non-belief causes moral decline is wrong. The opposite may even be true.