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

A similar saying that I think I picked up here would be, "I can explain it to you, but I can't understand it for you."

> 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."