Two people can disagree, argue and debate about a certain situation, and one of them may be a much better and more persuasive speaker, who can verbally transmit their ideas better than their opponent. There are techniques for making your opponent appear less correct and for placing your ideas in a better light in the minds of those judging the two debaters.
However, no matter how persuasive one is, if their ideas are incorrect, or inferior to their opponents, no amount of persuasion will change the outcome if their ideas are implemented. No matter how unlikable the person themselves may be, if there answer is correct, you should go with that one.