God gives us choice. He doesn't force his way on us. He gives us commandments and principles to follow because he loves us. Unfortunately, we live in a fallen world and people don't always make good choices. Thank God for His mercy and grace. Personally, I feel that the reason non Christian countries have less of a divorce rate is because they don't have the freedom. It's the culture in which they live in. In many of these countries if someone got a divorce they would not only lose a spouse, but their families would excommunicate them. These women would lose all their support. It's severely frowned upon and a person would bring shame to their family.
In some Middle East countries they would burn a woman to death, if she wanted a divorce. In some countries they don't even marry for love, but for money and status, so for them more is at stake. Just because some countries have less of a divorce rate doesn't make them a healthy home. These same homes have abuse, neglect, loveless marriages, and other sins. Many of these women in other countries feel like slaves and suffer in silence. They have no choice.
God is for marriages. It's suppose to be an example of how He loves his church/people. When two people make God the center of their marriage, it's a beautiful thing. Truthfully, the break down of the family is happening all over the world not just Christian countries.