I think when you "really destroy their argument," the average human bystander thinks "... what a jerk."
If you quietly make a few good points, don't push too hard, and ask sincere questions to help you understand the other person's perspectives, the average human will think "that guy is a class act. He had a good point, too."
Convincing anyone other than a hyper-rationalist of almost anything significant is more about emotions than it is about cold, hard facts.
And most humans, for better or for worse, are emphatically not hyper-rationalists.
It depends if your relationship with that other person exists in a vacuum or not.
If that other person is being manipulated by cult like behavior from some other party it can be very difficult to convince them of anything. The other party has no problem with lying then doubling down on the lies forever.
If you quietly make a few good points, don't push too hard, and ask sincere questions to help you understand the other person's perspectives, the average human will think "that guy is a class act. He had a good point, too."
Convincing anyone other than a hyper-rationalist of almost anything significant is more about emotions than it is about cold, hard facts.
And most humans, for better or for worse, are emphatically not hyper-rationalists.