The brief focuses on the second question before the Court which is:
[W]hether the Sixth Circuit erred by holding, in direct conflict with the Eighth Circuit, that state laws proscribing “false” political speech are not subject to pre-enforcement First Amendment review so long as the speaker maintains that its speech is true, even if others who enforce the law manifestly disagree.Or, as the brief puts it:
Can a state government criminalize political statements that are less than 100% truthful?
Ohio's law bans knowing statements of falsehood (or statements made with reckless disregard for their possible falsehood) that are intended to influence the outcome of an election. The CATO brief argues that this law violates the First Amendment and that the Court should "terminate it with extreme prejudice." By banning false statements in political contests, Ohio limits political discourse, which the brief argues is a loss for society:
After all, where would we be without the knowledge that Democrats are pinko-communist flag-burners who want to tax churches and use the money to fund abortions so they can use the fetal stem cells to create pot-smoking lesbian ATF agents who will steal all the guns and invite the UN to take over America? Voters have to decide whether we'd be better off electing Republicans, those hateful, assault-weapon-wielding maniacs who believe that George Washington and Jesus Christ Incorporated the Nation after a Gettysburg reenactment and that the only thing wrong with the death penalty is that it isn't administered quickly enough to secular-humanist professors of Chicano studies.
There are a lot of other good lines in the brief, so I recommend that you read the whole thing.