I think this is a shallow analysis. In the past and in many societies it’s fair to say that religion and social order were one and the same.

So it’s not wrong to say marriage has its roots in religion, but the cause to create marriage hasn’t gone away even if religion isn’t a factor: Can you imagine how difficult it was for a single parent (especially women) to raise a child alone, a few millenia ago? I think it’s fair to say that it caused major problems.

Even today raising children is still extremely difficult. Raising a productive citizen is another order of magnitude of difficulty.