Well, I think it should be Katarina and Talon, if anything was to form in their cold hearts.... Both assassins working for Noxian forces, under command of Katarina's father.
You can think of it in a sort of like Alexander Hamilton vs. Thomas Jefferson feud. The two men hated each other, but they were willing to work under the same roof due to Washington.
Take that away (following Washington's retirement) and the two basically tried to politically destroy each other.