Literally read the lore, anon. It's all explained right there.
Back in Shen and Zed's days as late teens, they were apprentices under Master Kusho, who was Shen's father and the leader of the Kinkou Order.
The Kinkou Order was an order of ninjas that were tasked to bring "balance" to Ionia when things get out of hand. They're basically Ionia's equivalent to the NYPD/LAPD.
They spent their apprentice years hunting down Jhin because he was a serial killer who was going around terrorizing the Ionian countryside by slaughtering merchants, famous artists/actors and entire farmsteads of people. The """art""" of the murders traumatized Zed on an irreparable level and it was the catalyst that essentially pushed Zed on the verge of insanity.
It took them 4 years to finally capture Jhin, and when they did, Kusho ordered the Ionian council to imprison him, rather than outright kill him. This was the final straw that broke Zed and caused him to defect from the Kinkou Order.