For all of his faults as king, this is the one thing that Robert gets right. As word first drifts back to Westeros that Daenerys has married Khal Drogo, everyone seems to take the news as nothing important. Even Ned makes a comment about her being just a little girl, so whats the big deal? In fact, it's not until half way through the fourth season that the small council mentions her again and Tywin begins to see her as the threat she really is. But Robert sees it much differently from the get go. He picks up on the fact right away that as long as a Targaryen heir is out there, theres a danger to the Seven Kingdoms, and to his rule specifically. Consequently, hes not going to sit by and just let that threat grow unchallenged. While its true that on his deathbed Robert does confess to Ned that it was a mistake to target Daenerys, the truth is Robert got it right the first time. Daenerys makes it clear over and over again that in her mind Robert sits on her throne. Hes the one that started the war against her family. Hes the one that lead to her family being killed and her and her brother Viserys having to flee. And she definitely has him and the Iron Throne in her sights. And so Robert should have gotten her out of the way as soon as possible. It may seem cruel to some that he actively plots the murder of a young teenage girl, but as the saying goes when you play the game of thrones, you either win or you die.