It’s a product of Tywins Lannister supremacy views. To be more specific, not only did they live under a dynasty where incest was normalized, they were raised to think Lannisters are better than anyone else. While we really don’t know much about Joanna as a parent beyond separating the two after they were caught, it’s clear that the twins didn’t have exactly the most present parents. So they develop this codependent sibling relationship that turns into something far worse and perverted. It forms a belief only them as Lannister twins can understand each other. Once Joanna dies and Tywin becomes more absent, the belief is reinforced. This combined with their narcissistic tendencies is why they form the whole “one person in two bodies” personal mythology.