There are several reasons that Junior may be cynical about his white teachers. One underlying issue is the history of what white people have inflicted on Native Americans during the last five hundred years—including forcing them onto reservations, denying their customs and beliefs, and forcing them to attend white schools.
In addition, the title of the book gives a clue: "part-time Indian" refers to the narrative voice of Junior being stuck between two cultural worlds. He is not Indian enough and not white enough—and sometimes people end up not liking themselves and projecting it into others. Junior may subconsciously hate the white part of himself in some situations, just as he might hate the Indian part of himself in others.
In chapter 4, Junior reveals some specific insights and perspectives regarding his white geometry teacher, Mr. P, whom he identifies with because they are both outcasts and eccentrics (Mr. P sometimes doesn't come to school and other times attends in his pajamas).
In the novel, there is a significantly large lack of trust from Native Americans toward "well-wishing but insensitive white people." Although Junior is excited about class and perhaps wants to like his teachers, he can't help but be cynical about them because of the long history of oppression faced by Junior's Indian culture.
This is why, during Junior's first day of geometry class, he throws a book at Mr. P's face; he sees that his mother's name has been written on the front page, meaning he's learning out of a thirty-year-old textbook. This is another example for Junior of "white lies" and the feeling of being unimportant and devalued as an Indian teen.
Sherman Alexie, the author of the novel, draws upon personal experience, as the book is semi-autobiographical.