Heh, well I think maybe you are trying to find logic where there is none
Seriously, those people who speak out against same-sex marriage as "breaking up families," "going against nature" blah blah blah really aren't opposing it out of any real logic, but are often parroting what their religion or culture has taught them.
For example, on your first point you talk about how same-sex couples with children will have children out of wedlock if same-sex marriage isn't legalized. The thing is that those who oppose same-sex marriage also typically oppose the adoption of children by lgbtq couples, lgbtq couples having children via sperm bank/in vitro fertilization/surrogacy. For them, under no circumstances should lgbtq couples have children or gain custody of children from previous marriages. When they talk about homosexuality breaking up marriages, they are talking specifically about heterosexual marriages. If a queer person comes out as queer when married within a heterosexual marriage, they would rather the person stay in the closet and remained dedicated to the heterosexual family unit than come out and "break up the family," nor should the person go from having "sinful thoughts," to actually performing the "sinful act." We are talking about people who refuse to accept our existence outside of a "sin" from which a person can be redeemed through religious observance.
As far as fractured families, a lot of these groups who talk about "modern fractured families" have a particularly glorified perspective of the past as a heteronormative paradise where "men were men, and women were women" (aka Archie Bunker). They view the "fracturing of the traditional family" as a result of civil rights, lgbtq liberation and women's liberation shitting on their big ol' heteronormative parade. If heterosexual families fractured, for them it's the fault of any sort of "rights movement," atheism, increasing sex/gender equality and so on.
They believe that homosexuality is the result of sin. A sinner can be redeemed if they confess the sin and refrain from committing it following repentance if we're looking at the Catholic faith, at least. However, if a sinner is unrepentant then they will spread their influence onto others. This is where the "corruption of youth" comes in. Queers can't be queer because "the children will be corrupted." Trans people can't be trans people, because "they will corrupt/rape/molest/convert the children." No same-sex couple can provide an "optimum environment," because they believe that the couple will drag the child down into "sin" with them.
Again, we're talking about people who use religion and the bible as their only frame of reference. We aren't talking about people who are going to debate through logical means.