In a story, the inciting incident is the event that draws the protagonist into the main conflict, disturbing their everyday world.
In The Absolutely True Diary of a Part-Time Indian, the inciting event occurs after Junior gets in trouble at school for throwing the geometry textbook at Mr. P. Rather than getting angry, Mr. P. apologizes to Junior, telling him that the reservation school is not serving him or any of the students well. Mr. P feels the poverty and hopelessness on the reservation tend to crush the spirits of young people, no matter how intelligent and ambitious they are. He uses Junior's smart sister Mary as an example of this phenomenon (though she is a talented writer, she stays in the family basement all day) and advises Junior that if he wants to ensure his future will not follow the same downward trajectory, he should try to leave the reservation as soon as possible.
The meeting with Mr. P. inspires Junior to take action. He decides to go to the local all-white school in order to obtain a better education, even though he will be an outsider there. This action pulls Junior into the main conflict of the novel, which sets Junior against both the prejudices of the all-white school and the prejudices of his reservation home.