Humiliated

"I humiliated him by expertly destroying his faulty logic."

From Merriam-Webster:

to reduce (someone) to a lower position in one's own eyes or others' eyes : to make (someone) ashamed or embarrassed

I think this one may be a little strong, but it would emphasize the faulty logic part (exposing it). It works well for describing someone in a group as well because it implies that there are others' opinions involved.

Humiliated

"I humiliated him by expertly destroying his faulty logic."

From Merriam-Webster:

to reduce (someone) to a lower position in one's own eyes or others' eyes : to make (someone) ashamed or embarrassed

I think this one may be a little strong, but it would emphasize the social aspect of exposing the faulty logic (i.e., being wrong publicly). It also works well for describing someone in a group because it implies that there are others' opinions involved.