Oblique request made without any explanation: can anyone provide examples of beliefs that are incontrovertibly incorrect, but which intelligent people will nonetheless arrive at quite reasonably through armchair-theorising?

I am trying to think up non-politicised, non-controversial examples, yet every one I come up with is a reliable flame-war magnet.

ETA: I am trying to reason about disputes where on the one hand you have an intelligent, thoughtful person who has very expertly reasoned themselves into a naive but understandable position p, and on the other hand, you have an individual who possesses a body of knowledge that makes a strong case for the naivety of p.

What kind of ps exist, and do they have common characteristics? All I can come up with are politically controversial ps, but I'm starting my search from a politically-controversial starting point. The motivating example for this line of reasoning is so controversial that I'm not touching it with a shitty-stick.