I hope that answered your question Patriot?
You have not answered a damned thing .
Yes I did. You asked this:
How, exactly would prohibiting same sex marriage ensure that all-or most children will have both a mother and a father?
Thank you.
And I answered you this in intricate detail:
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The state doesn't "insure" (sic), it
entices. States want to dangle a goody out there to entice the minimal number possible of children born to single people or to be in homes where either their mother or father are not present. And the reason states entice people this way is for the state's fiscal interest. States know statistically (not in each and every single case, but predominanty) that children grow up best and into the most well-rounded adult and productive citizens if they are raised in a home with both their mother and father present. Boys need a dad. Girls need a mom. It's all in the Prince's Trust link in the OP.
So a state throwing money breaks to a gay couple gets nothing but its own assured fiscal doom, statistically-speaking. You will counter with rare exceptions to the rule but the state when weighing its future finances is not going to be interested in looking at rare exceptions. It will do its calculations off of the preponderance of fact, not the rare exceptions to it.
So a state therefore has a direct, manifest and concrete interest in being able to regulate marriage so that its enticements do not have to be "legally forced" (by the fed) to go to fiscal pissing in the wind.
And that's just the emotionless fiscal argument. The psychological-stunting issue of kids raised in gay homes is an issue also of a state mandate in order to 1. Protect children from an anticipated harm (a thing they are required by federal law to do) and 2. To keep getting federal CAPTA money for insuring that children do not come to predictable and foreseeable harm.
There is nothing I can think of that is more damaging to a child than to live the daily example and message to them that "not only do you not have a mom (or dad), but that there is never ever even the remotest hope that you will ever have one: we are going to make sure of that." ....by the very structure of their relationship. Adults are free to have their sexual kinks. Only they cannot force a child-protecting state to play along to the absolute predictable psychological harm to children..
One of the number 1 issues of boys raised without a father or girls without a mother is indigency when they become young adults. And this rises from esteem issues of not seeing "themselves" represented in the daily adult world they grew up in. If they figure they don't matter, then applying for a job doesn't matter because who would hire a third wheel? etc. Imagine a boy raised in a lesbian home. How much do you think he would internalize "mattering in the functioning adult world" by the time he was 25?
There is a conflict, a direct conflict between the federal CAPTA guidelines and the mandate of "gay marriage" across the 50 states. It's right in the OP. Even a half wit lawyer could read the fine print and have a case.