We all know that Jaime Lannister got his nickname, Kingslayer, when he dropped the Mad King like a bad habit. That was after the King, Aerys Targaryen, flambeed a bunch of people he considered traitors and before he could execute his plan to turn King's Landing into a smoldering pile of ash with vast stockpiles of wildfire hidden around the city. Of course, Cersei Lannister managed to make use of the wildfire when she blew up the Sept and a bunch of her rivals.
“I mean I don’t think he — I’m just saying it’s a valid theory,” Coster-Waldau told Mashable. “I can see it makes sense, it has a beautiful — it’s a nice circle [that] they are born together in the womb and then he kills her at the end…It makes sense."
You'll recall that Jaime killed the Mad King for suggesting the use of wildfire against his own people. Cersei literally did that.
“You could say that could — that the motivation for doing that would be the same for killing Cersei, but I haven’t seen anything yet before Season 7 that would make me believe that he was capable of doing that,” he told Mashable.
We don't know about this. Game of Thrones fan theories have been kind of stunningly accurate when they're not suggesting things like that the Ironborn are going to summon Cthulhu from the deep. This seems within the realm of possibility, especially given that the show has been prone to off key characters at critical moments.
Jaime and Cersei probably long for the halcyon days of just crippling Bran Stark to cover up their incest. Given all their mutual betrayals, Cersei's seeming madness, and their love for each other, the issue of what to do about Queen Cersei seems like an intractable problem. Alexander the Great faced just such a problem with the Gordian knot. He solved it with a sword.