Some fans suggest that Tyrion is not Tywin’s son, but the son of his wife Joanna and the Mad King. It is known that the Mad King really had an interest in Joanna, and if Tyrion is his son, that would explain Tywin’s hate for him and constant anger toward the Mad King. Additionally, this would explain Tyrion’s obsession with dragons that he’s had since he was a little boy and the fact that Dany’s dragons once showed their favor to him.

And this actually would make him another true heir to the Iron Throne. Many fans agree on the thing, that we won’t see Jon or Dany getting the Throne since it would be too obvious — and obvious definitely isn’t Game of Thrones thing. So the creators really need someone else to rule, and actually, someone who people like, and Tyrion makes the perfect candidate.