First, I disagree with his assumption that a successful persuasion roll would "win them over to his side." That's not persuasion, that's mind control. Persuasion doesn't work that way.
However, I would've let him make the roll with a negative because he's already stated his case and been rejected, now he's fighting an uphill battle. If he was successful in the followup, then I, as GM, would state to the party, "Well, he does have a point", and let them debate it from there.
But he wouldn't have "won them over" simply because he made a persuasion roll, which is what it sounds like he wanted to do.