It seems you wish to demonize the historical origins of the gay rights movement because it does not correlate with your vision of marriage being a particularly family centered institution. Regardless of whether same sex couples are allowed to marry or not, marriage has already been radically transformed to the point that only 25% of the families in our country represent the traditional nuclear family. Same sex marriage promises to increase the number of 2 parent homes in which children could be raised, and if the latest 35 years of research is any indication, having 2 parents is considerably more important than the gender of the parents. Furthermore, as many as 8 million children are being raised by gay couples and same sex couples and all of those could benefit from the institution.
Regardless of how you feel about the historical motives of the gay rights movement, the family benefits of marriage will exist within same sex marriage. As such, you have no rational recourse in which to deny same sex couples the right to marriage.