That was the trigger.
There is a difference between reason of something and the trigger for something. From Rin's death he basically saw the corruption , but just had a bad way of going about things.
His reasons : Corruption. He had already stopped caring for this corrupt world, where kids were forcefully made jinchurikis. (Something the Shodai tried to get rid of)..
Kabuto's trigger is him killing his "mom"
Madara's trigger is the death of his brother and not being hokage.
Sasuke's trigger was the death of his brother.
Naruto's trigger is the death of Jiraiya.
Hashirama's trigger is the death of his brothers.
But are those their reasons for what they are doing? no... simply their motivators or what pushed them into what they are currently doing.
Peace is his goal:
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