The idea that a woman should only breed with one man, who will then assist in the protection and care of resulting offspring, predates both government and religion (even if one accepts Genesis, I don't think it claims the continuous existence of religion between the time of Adam and Moses; if a proper religious tradition already existed, it would not have been necessary for God to instruct Moses in writing the Torah).
Religious arguments against marriage are counterproductive in talking with anyone who does not accept the religion in question. The secular argument is much stronger: 99.99999% of all people who have ever lived, lived in a society which recognized a concept of marriage involving exactly one male as different from any kind relationship involving any other number. The requirement that marriage involve exactly one male is not imposed by government, nor by religion, and the only way it can be viewed as "bigoted" is if the vast majority of people who have ever lived are bigots.
Further, even if gays have the right to call themselves whatever they want, that does not imply that anyone else has any obligation to honor such declarations. The right of free association implies the right to honor the kind of marriages that has essentially always been nearly universally recognized, without incurring any obligation to recognize so-called "marriages" which fail to meet one of the most basic and universal requirements of marriage (that it must involve exactly one male)
“...even if gays have the right to call themselves whatever they want, that does not imply that anyone else has any obligation to honor such declarations...”
If the issue about same-sex marriage were really about marriage, then you would be right, but sadly it is far more about forcing Christians to approve of homosexual relationships than it is about marriage. Otherwise, why would there be any problem when a Christian wedding photographer politely declines to throw his creative talents into recording a same sex wedding? Why grind a Christian baker into the ground and force him to close his business because he declined to sell a same-sex couple a wedding cake? Because gays demand something that people like me cannot give them, approval of their immoral acts and especially to grant them equal status as “married”.