This is where I see a major fallacy:
No fallacy.
How does allowing homosexuals to marry effect a woman's inherent right to motherhood or ability to get married? I mean, gays aren't exactly going to go around and say - damn, can't marry my true love, guess I'll just go pick up a woman.
It doesn't.
The question you should be asking is why attach a legal imprimatur to something that does not result in a right to motherhood and the family relations consequent to it?
As far as children - I have yet to see any reliable research conclusively show that being raised in a homosexual household is damaging by reason of homosexuality alone.
A right to motherhood is not limited to the act of procreating alone. It has much to do with the relationship of the mother and her child. We, as a society, are very much concerned with our children. In fact, regardless of cultural background, this care can be considered universal. And so, we institute laws that govern not only the children, but the process by which they come to be. No other human relationship other than the conjugal relationship between a man and a woman creates another human being - someone who never consented to anything, is utterly dependent on the family he finds himself in, and YET INCAPABLE OF HELPING HIMSELF.
I have no intentions of questioning the reliability of the research you mentioned and its conclusions. However, I think society is WITHIN REASON to hold the family relations that result in marriage to a higher standard.