Why did Nagato make Payne Six Paths?

The Payne Six Paths all have one thing in common, that is, except Yahiko, all six of them have been met by Jiraiya, and some have even fought against each other.

However, Nagato found these five people to make the  Payne Six Paths and used them to fight Jiraiya in order to prove that he is a "god"-like existence in this world.

He wanted to prove to Teacher Jiraiya that this world is full of The painful thing is not that it is full of love in the world as written in "The Legend of Genshin Ninja", which proves that Jiraiya's point of view is wrong, and this is what Jiraiya finally risked his life to prove.