Marriage does provides a stabilizing effect on the overall society, divorce negates that stability. While there is a time and place for divorce, what is good for the individual isn't always good for the group.
Stabilizing effect? How so? Single people are a danger to society?
Potentially. French author Michel Houllebecq makes a typically misanthropic case.
In paraphrase, marriage is, fundamentally, a tool for creating a fairer mating market. Resurgence of the ordinary primate mating behaviors--a free mating market--in humanity is at least cause for concern, because free markets always have losers. Extension du domaine de la lutte, indeed.
I don't know how much I agree with this, and although there's an element of truth to it, it characteristically ignores the infinite variations of human motivation, taste, and personality.
I am not familiar with that hypothesis, but if you've represent it correctly and I've understood it correctly, it's total bullshit. It is based on a number of generalizations about the human race that are simply not true:
1) that marriage is an assurance of 'mating' - no, it is not. One or both partners might be either uninterested, unwilling, or physically or psychologically incapable to have sex. (Or to have an emotional relationship, for that matter.) If one partner wants sex with the other and the other does not want it, well, tough luck, but the former will have to deal with it, and can't force the other partner - fortunately, rape in marriage is recognized in many legal systems today.
2) that marriage is an assurance that neither of the partners will 'mate' with other people - c'mon, we all know that's not true.
3) that everyone is monogamous, and that everyone wants to be married in the first place. Not true. Some people prefer casual relationships, some people will have relationships with multiple partners, some people regard themselves asexual, some people can't stand or aren't able to have relationships at all...
4) that people just care about 'mating' about ANYONE, rather than WHO they will 'mate' with. Not true. Maybe there are people who just want to be with anyone - actually, I am sure there are, there are lots of people who'll have sex, date, or even marry anyone, so they wouldn't be alone - but lots of other people are selective and if they are just not into someone, they'll rather masturbate and fantasize until someone they actually like comes along.
In short, human 'mating' is not nearly as simple as that hypothesis assumes, and the hypothesis would work only if all the above were the case... but none of it is, which means that the existence of marriage in itself doesn't solve anything, and married people aren't automatically more successful or satisfied in their private life, or in any way superior to single or divorced people.
It's just that religion isn't as powerful thing as it is now. It's waning now, people are more rational now, so it makes sense to see that in another 400 years time, it will have decreased.
It's waning? Are you serious?

Have you ever watched the news?