After the state Supreme Court ruled same-sex couples could wed, California voters enacted the ban with 52 percent of the ballots in November 2008.
But a federal judge struck Proposition 8 down in August, saying it was unconstitutional discrimination. The ruling was stayed until the appeals court rules.
The appeals court is looking at two issues: whether the referendum's defenders have standing to take it to court and whether Prop 8 is constitutional.
Monday, attorney Charles Cooper, representing those defending the ban, contended marriage exists so society can establish a relationship between a man and a woman that can lead to children, the Los Angeles Times reported.
"When a relationship between a man and a woman becomes a sexual one, society has a vital interest," Cooper said.
But Judge Stephen Reinhart, the most liberal member of the three-member panel, said, "That sounds like a good argument for prohibiting divorce. But how does it relate to having two males or two females marry each other and have children as they have in California? I don't understand how that argument says we ought to prohibit that?"
The Times reported Judge N. Randy Smith said same-sex couples have all the rights of marriage except the word "marriage." He asked how Prop. 8 protects marriage given that situation, the Times reported.
"You are left with a word, but a word that is essentially the institution," Cooper responded.
Both outgoing Gov. Arnold Schwarzenegger and Governor-elect Jerry Brown have declined to defend the ban. The newly elected attorney general, Kamala Harris, also says she won't defend it.
"We will not defend Proposition 8. It is clearly ... a proposition that was found by a judge to be unconstitutional," NPR quoted Harris as saying. "And we should not use the limited resources of the state to defend a law that has been found to be unconstitutional, and I will not."
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