This is somewhat of a misnomer, since a "self-hating Jew" is usually not someone who really hates themselves. Rather, they identify themselves as more than, or something other, than just a Jew. They view themselves as a regular human being first, and feel uncomfortable with Jewish ethnocentrism and the "Chosen people" stigma. Even though they were born to Jewish parents, they are in direct opposition to religious Jewish dogma which they see as outdated and limiting. They may even believe that by setting themselves apart throughout history, the Jews may have unwittingly brought antisemitism unto themselves.
Self-hating Jews long to be Gentiles, because they do not like the designation and tradition forced on them by their ancestors and/or religion, which they have shed. They find liberation from their "self-hate" by identifying themselves not exclusively as Jews who are "strange" and "different", but as Gentiles; as any human being; no matter the race.
Jew #1: "The Nazis were overzealous in their logic which brought around their own demise. But some Jews also display the same racial, "pure-blood" thinking, which may have contributed to THEIR demise. It exposes a duality, a flaw in human nature: ethnocentrism is a flawed concept that can hurt anyone, no matter their race. This is 2011, its about time we advance beyond racial thinking"
Jew #2: "How dare you say that Jews brought the Holocaust onto themselves? Have you no pride?"
Jew #1: "Dude I didn't even say that. Besides, I do have pride, it is individualistic pride. I think for myself and I don't understand the concept of collectivist Jewish pri-"
Jew #2: "Stfu man. You're such a disgrace, you're nothing but a self-hating Jew"