Demacia believes in justice and order, and Noxians believe in freedom from control, and the ability to seize power for yourself. Kayle's family believes pretty much the same thing as Demacia, and Morgana believes pretty much the same thing as Noxus. There has always been two sides of the coin, so to speak. So if the Kinkou Believe in balance, it would make sense that Zed strives to ruin that balance. But why?
Maybe Zed saw the darker side of the Kinkou. They are neutral. They sometimes to morally questionable things to preserve the balance. It would make sense then, that something they did to keep balance, ruined Zed's Life. Maybe they killed someone he cared about, causing him to slowly fall into darkness.
Another possibility is he could have been part of the Kinkou, but was kicked out due to breaking their laws, only to be replaced by the new three. Once again, this gives him motive to try and end the Kinkou's efforts.
In the end, this post will probably mean nothing, as i'm sure Riot already has the lore, but it's still fun to guess.