In November of 1998, George R.R. Martin published the second in his A Song of Ice and Fire series, A Clash of Kings. In it, Daenerys walks into the House of the Undying and sees a flurry of visions, including one of her late older brother Rhaegar, his wife Elia and their newborn Aegon. At the end of it, Rhaegar turns to her and says: "The dragon has three heads." From that scene came what is now known as the Game of Thrones Tyrion Targaryen theory.
In the intervening 19 years since that book came out, fans have speculated who that third head was. Clearly the first is Dany, and she will ride Drogon. (Even when Drogon was small, her affinity for him stood out.) Obviously the second in Jon Snow, who is a sekrit!Targaryen, because someday we would learn that R+L=J, making him a Targaryen. But who was the third rider?
The most popular theory is that there was an other sekrit!Targaryen running around in the story. Someone who was a POV character from the beginning, like Jon and Dany. Someone who's parentage could be questions because of weird hints Martin dropped in the books.
Of the POV characters we meet in the first novel, Ned and Catelyn are dead. Sansa, Bran and Arya are trueborn Starks, and no one questions that. Which leaves on answer: Tyrion.
And then, this week, we learned the truth. There is no third rider, at least not a living one. Whatever Rhaegar meant, it wasn't that.
And so, after 19 years of speculation about Tyrion's "shock of blonde hair so pale it was practically white," his "single eye so dark it was almost purple," or debates about "what Twyin meant" when he said that Tyrion was no son of his, it's all over. Whatever liberties Aerys Targaryen took with Johanna no longer matter. Tyrion's rapport with the dragons in Meereen aren't a sign of anything, except a degree of being very good with animals.
We no longer need a third dragon rider. Dany will ride Drogon, Jon will ride Rhaegal and the Night King will ride the ice dragon once known as Viserion. And that means that Tyrion, despite his clear longings for Daenerys and his love of dragons, is most likely not a sekrit!Targaryen running around. (After all, one is excusable. Two begins to look like carelessness.)
Maybe it will still turn out that he is, after all this time. But personally, I like Tyrion as a legit Lannister. It makes everything just that much more tragic, both about how his family treats him, and how much he still cares for them, despite it all.