When someone says something like "The left went crazy and drove me to the far right!", they're not (usually) relaying a neutral history of their intellectual development. Same when they reply to your post about animal welfare claiming that it "made them want to eat meat even more."
Instead, what they're usually doing is two things:
The threat and/or cheer-leading gains credibility by not being explicit about the motivation, and portraying it as an uncoordinated decision. But that also means that explaining to the person that rational people don't get negatively polarized is unlikely stop them from saying these bizarre-sounding things.
To evaluate this, you need to have known that person in the past. I know some people who say stories like "I was always X, but recently I have suddenly switched to Y", but I also knew them a few decades ago and their attraction towards Y was always there, so that hearing about them switching to Y came as no surprise to me, or rather only the specific timing was surprising.
People seem to be quite bad at knowing what made them do what. Many of their beliefs are just post-hoc rationalizations.