The three-judge panel is considering two challenges to the law approved in California last fall. It took no action Wednesday and will issue a written ruling later.
The law was to go into effect Jan. 1, but the court put it on hold pending its decision.
Chief Judge Alex Kozinski noted the U.S. Supreme Court struck down a California ban of violent video games because the state failed to show a compelling reason to infringe on game-makers free speech rights to manufacture the products.
He said it appeared the same argument could be applied to the evidence lawmakers relied on in passing the prohibition on sexual-orientation change therapy.
"We really don't have anything compelling, as I see it," Kozinski said. "Government has to have a compelling interest in curtailing speech."
California Deputy Attorney General Alexandra Robert Gordon, who is defending the ban, cited mainstream medical organizations' support of the law, and testimony before the state Legislature by several people who said they were harmed by the counseling.
Kozinski replied that opponents of the law also testified before lawmakers that they benefited from the counseling.
"There is evidence going both ways," Kozinski concluded.
Lawyers for parents of children who are undergoing the counseling and licensed professionals who administer the "talk therapy" argued the ban goes too far. But Mathew Staver, founder of the Liberty Counsel and a lawyer opposing the law, said there is "no evidence of harm."
The law says therapists and counselors who treat minors with methods designed to eliminate or reduce their same-sex attractions would be engaging in unprofessional conduct and subject to discipline by state licensing boards. The activities of pastors and lay counselors who are unlicensed but provide such therapy through church programs would not be covered.
The cases before the appeals court was brought by professionals who practice sexual-orientation change therapy, two families who say their teenage sons benefited from it, and a national association of Christian mental health counselors. They argue the ban infringes on their free speech and freedom of association and religious rights. The counselors also argue it jeopardizes their livelihoods.
"The state has determined that the only permissible message (is that) same-sex attractions, behavior or identity are to be accepted, supported and understood, thus suppressing all other viewpoints to the detriment of licensed professionals and their vulnerable minor clients," lawyers for the families, several practitioners and the professional group said.
"The viewpoint of counselors who in their professional judgment determine that same-sex attractions conflict with the religious and moral beliefs of clients and are not desired, is silenced by SB 1172. This raises a serious constitutional question."
Supporters, including Gov. Jerry Brown and Attorney General Kamala Harris, say the prohibition on "reparative" and "conversion" therapy is necessary to protect children from a coercive practice that can put them at increased risk of suicide. They also say the therapy's efficacy has been questioned or rejected by every major mental health professional association.
Harris has argued the law "is based on a scientific and professional consensus reached decades ago that homosexuality is a normal expression of human sexuality and not a disease, condition, or disorder in need of a 'cure.'"
Reflecting the competing issues before the appeals court, the two Sacramento-based trial judges who handled the lawsuits in December reached differing conclusions on whether the ban violates the U.S. Constitution.
One refused to block the law after ruling the plaintiffs were unlikely to prove the prohibition unfairly tramples on their civil rights and should therefore be overturned. The other said he found the First Amendment issues presented by the ban to be compelling and ordered the state to temporarily exempt the three people named in the case before him.
The panel hearing the cases Wednesday consists of Chief Judge Alex Kozinski, who was appointed by Ronald Reagan in 1985, Judge Susan Graber, a 1998 Bill Clinton appointee, and Judge Morgan Christen, a 2012 appointee of President Barack Obama. The judges have no deadline for issuing a decision.