This is kind of obvious but whatever.
As we have seen from manga 607 Nagato first rejects ( or Yahiko forces Nagato to reject ) Tobi's proposal in teaming up to help Nagato master the rinnegan.
They most likely continue to reject Tobi's ideals until Yahiko dies.
After Nagato's rampage he remembers what Tobi told him, and goes running to Tobi about this world with just peace and all love. And bam, Tobi starts his series of manipulation.
TL;DR: Yahiko's death
Maybe we will have some flash back where Nagato comes up to Tobi saying " Tell me more about this world..." Then they both walk off into the distances.. DUN DUN DUN.