Gay people are more likely to explore extramarital affairs than heterosexual couples. Therefore, allowing them to marry would undermine the fidelity of marriage.
In a recent survey, more than 79% of heterosexual men and women and lesbians in civil unions said they strongly valued sexual fidelity. Just 50% of gay men said the same. This illustrates the disregard for sexual fidelity among the gay community.  Sexual fidelity is a widely accepted and celebrated norm of marriage. To allow homosexual couples to marry or enter a legally recognised union would be at best a disregard to marital fidelity, and at worst an endorsement of infidelity.
We allow serial cheaters to get a marriage license and marry a new partner. The government’s role is not to uphold the fidelity of marriage. Additionally, this argument does not rule out allowing gay people to enter civil partnerships.
[P1] Fidelity is an essential component of marriage. [P2] Gay people are more likely to have extra-marital affairs than heterosexual couples. [P3] To allow gay people to enter the institution of marriage would undermine the fidelity of marriage. [P4] Therefore, gay people should not be allowed to marry.
Rejecting the premises
[Rejecting P3] The government's role is not to protect the fidelity of marriage. [Rejecting P4] Gay people can still enter civil unions or partnerships.