The conflict of a story is defined as the struggle between opposing forces. One way to simplify the struggle is to determine if it is man vs nature, man vs man, man vs self, or so on. For John and Lorraine in Zindel's The Pigman, the conflict is man vs man because these two protagonists both struggle with their relationships with their parents. For example, John calls his father "Bore" because they are always arguing about the way John should behave. Lorraine's mother continually tells Lorraine whom to trust, how to act, and what money not to spend. Neither of these home environments create an atmosphere of love and understanding in which grown teenagers can thrive. As a result, they latch onto the kindness they find with Mr. Pignati.
Mr. Pignati is also a protagonist, and his greatest struggle is admitting that his wife actually died and is not on vacation in California. This could be categorized as man vs. self because he has to admit the truth within himself in order to satisfy the conflict. It takes his friendship with John and Lorraine to help him admit to himself that his wife is truly gone.
In an interesting twist, however, the conflict turns from the three protagonists against the world to Mr. Pignati against John and Lorraine. When the teens have a party at his house while he is in the hospital, the place gets trashed and he comes home early to see it all. He feels betrayed by John and Lorraine, but they apologize and he forgives them. Overall, though, John and Lorraine's main conflicts are with their parents and Mr. Pignati's is with himself.