Bishop Salvatore Cordileone has said that the gay marriage debate is not about equality under the law.

Cordileone, an outspoken opponent of gay nuptials who in 2008 backed passage of Proposition 8, California's ban, was recently installed as the leader of the Archdiocese of San Francisco. He is also the chairman of the U.S. Conference of Catholic Bishops' (USCCB) Subcommittee for the Promotion and Defense of Marriage.

In a blog post at the USCCB's website to promote the church's understanding of marriage, Marriage Unique for a Reason, Cordileone criticized President Barack Obama's inclusion of marriage equality in his inaugural address.

Obama cited Stonewall, the birthplace of the gay rights movement, and stated that “if we are truly created equal, then surely the love we commit to one another must be equal as well.”

“I honor the president's concern for the equal dignity of every human being, including those that experience same-sex attraction, who like everyone else, must be protected against any and all violence and hatred,” Cordileone said.

“But the marriage debate is not about equality under the law, but rather the very meaning of marriage. Marriage is the only institution that unites children with their mothers and fathers.”

“Protecting this understanding of marriage is not discrimination nor is it some kind of pronouncement on how adults live out their intimate relationships; it is standing for the common good,” he added.

(Related: Salvatore Cordileone: Gay marriage wins are a call to “defend marriage.”)