There are people who really believe that making gay marriage legal will make their own heterosexual marriages less meaningful. The two arguments that I have heard:
(1) Marriage represents a relationship between God and two people. Homosexuality is a sin, so God would not recognize a marriage between gay people. If you allow gay marriage, you are therefore taking God out of marriage which hurts the very idea of marriage and thus damages marriages for all people.
(2) In legal documents, if only straight marriages are allowed, you can refer to the participants as "man" and "wife". If gay people are allowed to be married, then marriage certificates issued by the city/county/whatever would become something like "person 1" and "person 2". Having a marriage certificate that does not refer to a straight couple as "man and wife" takes away something (?) from the marriage.
People also use the idea of marriage = God + man + woman to argue that gay people should not want to be married since they cannot have a real marriage without God. I am not sure what they would have to say about atheists getting married. I am also not sure why they think a certain religion "owns" the idea of marriage (not all religions view marriage as a religious act).