Phrasing the challenge as "sound enough logic" puts the burden of proof in the wrong place. It implies that whenever you're not persuaded it's the fault of the other person for not being persuasive enough. That's the opposite of open-mindedness. It is exactly because of the presumption that your current beliefs are true that you won't change your mind as easily as you might think. Even Scientologists say they'll leave the church if somebody could just provide them with evidence it's all baloney, but it's a standard of proof nobody can meet.
When I say all persuasion is repetition, it's really not an overstatement. Maybe you're closer to believing me this time ;-)