You can't reason someone out of a position they didn't reason themselves into.

I don't think this is empirically true, though. Suppose I believe strongly that violent crime rates are soaring in my country (Canada), largely because I hear people talking about "crime being on the rise" all the time, and because I hear about murders on the news. I did not reason myself into this position, in other words.

Then you show me some statistics, and I change my mind.

In general, I think a supermajority of our starting opinions (priors, essentially) are held for reasons that would not pass muster as 'rational,' even if we were being generous with that word. This is partly because we have to internalize a lot of things in our youth and we can't afford to vet everything our parents/friends/culture say to us. But the epistemic justification for the starting opinions may be terrible, and yet that doesn't mean we're incapable of having our minds changed.