Great bumper sticker, terrible in practice. If someone has a sound base of knowledge and they are challenged by someone who doesn't, they should not change anything.
They should change their approach. Everyone thinks they are right. Everyone thinks their knowledge is sound. We live in a world where everyone thinks everyone else is stupid, they rarely apply that label to themselves, and when they do it's usually a sign of embarrassment, not a confession that they are aware that they possess inferior reasoning.
What you mean to say is that if someone as capable of producing a superior argument from an objective standpoint they should be acknowledged as superior without further questions. May I point out that at one point there was a superior objective argument in favor of eugenics. It took a World War and attempted genocide to refute that particular argument. Everything should be questioned all the time by everyone. Not everyone does this, it still doesn't mean they should have questions imposed upon them. Those who choose to think will think, those who choose to follow will follow, those who choose to rebel will rebel. All of these behaviors are necessary to forming, improving, and discarding ideas.
Your idea isn't superior because it's yours, it isn't superior because it seems sound, or even because the most educated among your contemporaries agree with you. It is only superior if it takes hold and lasts long enough to inspire new and better ideas. It is time and popular participation that sorts crap ideas from brilliant ones. Socrates was the one that pointed out that a wise man doubts and a foolish man claims to know. Forming knowledge is a process to participate in, not an achievement to gloat about. There is always another unknown beyond the horizon that threatens to change everything.
Knowing yourself, the weaknesses of your own reasoning, and maintaining the flexibility to change your understanding as new information becomes available is the only way to participate in the formation of knowledge in a progressive way, otherwise you become just another road block that the rest of us must navigate around. No worries though, we do know how to navigate around road blocks, we are flexible and willing to understand you, even if we don't agree.