That is, speaking very charitably, a non-sequitur. There are all sorts of reasons children are raised in families that don’t include “a mom and a dad”; Dolan must know that. Same-sex marriage isn’t one of them.
Maybe Dolan believes that divorce, in any circumstance, violates a child’s rights; how about children adopted by gay parents—does he believe that their rights would be protected by lingering in foster care, bounced from non-home to non-home?
Would he prefer that those born to gay or lesbian parents had never existed? If so, that is a pretty tangled position for a Catholic (or even for a writer of North Korean communiqués).
Does he think that children should be taken away from gay parents (or single widowed parents, for that matter) who have loved them all their lives to be given to any heterosexual, or even just heterogeneous, couple?
And even if he agrees with all of that, what on earth does it have to do with same-sex marriage? Allowing two people who love each other to marry will not stop people who don’t love each other from separating, or from getting married in the first place. Neither marriage nor love is a scarce resource. And yet Dolan talks as though there were thieves in his house.
If one’s only interest in all this is the rights of children, then gay marriage is really an imperative. (There are other factors, too, of course, that don’t depend on children: respect, fairness, kindness.) Marriage can protect children—legally, financially, socially—and same-sex marriage will give more parents more ways to protect more children. Making that possible is surely the right thing to do.