At least in this country, the biggest benefit of marriage for children is that it highly increases the likelihood of fathers' actually being involved in the kids' lives. In this country, future poverty, involvement in crime, and low education really unfortunately go hand in hand with marriage. No, marriage isn't a panacea that automatically fixes those problems, but it's so deeply entrenched. There are tons of studies out there that try to figure out the why's. This is not to say that people who co-habitate can't elect not to marry while also raising a good foundation for children at home. If everything else is the same, there's probably no observable difference in how children are raised. However, in practice, that simply isn't the norm in this country. If I had to guess, I'd say co-habitating couples who raise children probably eventually move on to marriage, but the ones that don't often end up with children who only have one parent (usually the mother) raising the kid on her own. I think it's really pessimistic to think that people who feel emotional benefits of marriage have "false beliefs."