If you ask someone "why?" enough about a subject you don't agree on, eventually both of you will come to a conclusion
Many hold strong beliefs and opinions, however not many know the roots of their belief. If a person agrees to explore it, both of you will learn something new and fascinating. The problem is finding someone who wants to think and ask the questions. This goes for both. Many want to "convince" someone, but how much do you truly know about the thing you're trying to prove?
This also comes back to the "why?" game so many kids play. Parents get annoyed by it, but are they really annoyed at the game or their lack of knowledge depth? Play the game, find out how deep you lake of knowledge goes
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But not necessarily an agreement.
I remember asking my father in law why he doesn't believe in climate change. It boiled down to him saying the democrats just want to control us. When I asked why he said just so they have more power for power's sake. I told him I'm willing to accept that politicians can be like that (because many are) but why does he believe that the republicans are immune to this craving of power or if he thought republicans denying climate change could be just for the sake of controlling people to get more power (like he accused democrats of) and surprise surprise he couldn't give me an answer other than democrats are corrupt and want more power but republicans don't (which isn't an answer because I'm asking why).
Turns out most everyone thinks based on reasoning developed by years of cumulative, biased experiences that ultimately amount to fundamentally distinct axioms of how the world works. Few people actually have opinions based on "logic", least of all the people who fly the banner of "rational" or "emotion free" opinions. Answering why just provides post-hoc explanations rather than an actual cause (which humans are great at coming up with, just look at split brain cases). Which just turns most "big topic" disagreements into competitions over who can come up with a better sounding justification.