Everyone tends to assume that they are right (and not for the wrong reasons). If you're tied to the big-government/small-government dichotomy, you might well consider dictatorship as being tied to "excessive safety nets" than to rather more pointed concentrations of force that (you imagine) will not impact your personal life negatively.
And there's no real continuum of opinion, any more, with the centrist POV having been pulled apart like a old bit of taffy, so those who you might listen to and hear a slightly offset viewpoint which you're willing to consider (and maybe adjust to) don't really help you bridge the gap to the other side. Everyone on the left/right is apalled/disgusted/annoyed/amused by what it seems everyone on the right/left is saying, and there's little meeting of minds.
There can be, of course, but then there are voices from the outer fringes which discourage good old traditional cooperation and compromise. And one fringe in particular seems (to me) to be most discouraging, but that might just be the current political dynamics as they slowly flutter through history.
Hard to pick apart the honest beliefs (whether or not 'honestly' posed to them to start with) from your basic performative exageration, though. I'm not sure how I'd behave if asked to present a vox-pop statement, when I wasn't certain whether it'd attributively pop up in sight of my neighbours (or even if I was rather hoping if it was), having the impression that they might judge me (for well or ill) on how much I amplified their apparent position. I've had a friendship with someone vastly opposed to many of my own views, and I was always (too much, really) unwillingly to outright disagree with them.
Then there's my opinions on political "I'm supporting <Foo>" signs. Thankfully rare, around here, but imagine being the only one not displaying signs of the given hue (or any signs at all) in some neighbourhoods. I haven't been anywhere that confidently and materially contrarian/abstentionist, possibly, since I steadfastly claimed that I didn't have an average number of legs (my recollection being that everyone else said they did) in a maths lesson.