> I always interpreted it more as saying that the person has to reason themselves out of their position.

But that interpretation would make the second half a moot point, wouldn't it?

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

If you want to say a person can only reason themselves into any position, it could become "You can't reason someone out of a position."

No because I believe you CAN reason a person out of a position they reasoned themselves into, but if they hold a position that they DIDN'T reason themselves into, THEY have to do the reasoning.