What can you compare about Jack and Piggy?
I'm trying to use this quote: If you hate a person, you hate something in him that is part of yourself. What isn’t part of ourselves doesn’t disturb us. –Hermann Hesse, Demian
Can this be applied to Jack with Piggy?
I think Jack and Piggy are almost absolute opposites of each other.
For example, Jack's ownership of the hunting brigade demonstrates what might be apparent physical fitness and prowess in him. Piggy is the absolute opposite. Whereas Jack has no problem removing his clothes to reveal the inner man, Piggy is ashamed of his apparent fat and asthma.
Also, Piggy's intellectual ability intimidates Jack. When Jack fails to become the leader, there is something in him that really struggles with that, but he does not have the intelligence to thwart the boys' purpose for choosing Ralph. Piggy thinks through all circumstances and comes to Ralph's right hand as a sort of advisor. Jack might like to be that person, but he doesn't know how to communicate with reason and logic the thoughts that are inside of him.
To apply the quote you cite in your explanation, you might look at how each character uses their ability to try to seek leadership or at least approval among the boys. Jack tries to portray how what he is interested in will provide survival and sustainment for the boys in finding meat. Piggy, likewise, tries to demonstrate that proper hygiene, developing shelter and seeking to be rescued are keys to maintaining survival. Piggy and Jack hate the leader in each other because their leadership styles and motive are different but seek similar outcomes.
Another part of Jack's character that has nothing to do with leadership may not only be not disturbing to Piggy but acutally appealing. The converse may be true too. Consider if there might have been a scene wherein Jack led the choir in song. Piggy might have thoroughly enjoyed it. He would have enjoyed it because there was no room to compare himself to Jack. In the field of music, Piggy may not be gifted.