"Why does Judaism exist?"--Ask Abraham, Isaac, Jacob, Joseph,Moses, Isaiah, Jeremiah, Hillel, Christ, Maimonides, Spinoza....

"Should Judaism exist?"--Again, ask Moses, David, Solomon, the Maccabees, Herod, Christ, Maimonides, Spinoza, Marx (and the Marx Brothers), Trotsky, Freud, Adler, Mahler, Leon Blum, Billy Wilder, Andre Kertesz, Robert Capa, Leo Szilard, Edward Teller, Robert Oppenheimer, Richard Feynmann, John von Neumann, Eugen Vigner, Arthur Koestler, Sam Goldwyn, Irving Thalberg, Adolph Zukor, Steven Spielberg, Woody Allen, Sidney Lumet, Seinfeld and these Jewish comedians: https://www.ranker.com/list/list-of-famous-jewish-comedians/famous-jews

Without us the last century would have been laughless and you lose 22% of all Nobel prize research.

Your civilization and Jewish thought are inseparable. Get over it.

The IHRA's definition of anti-semitism includes your two questions because you didn't ask:

Should Christianity exist?

Should Islam exist?

Should Buddhism exist?

Should Hinduism exist?, etc.

If you question the existence of Jews without doing so to all of the above, you are an anti-semite by any reasonable measure.

And here is your fate: extinction, along with ancient Egypt, Assyria, Babylonia, Seleucid Greeks, Romans, Byzantines,Omayyads, Abbasids,Fatimids, Mamluks, Ottomans, the British Empire, the USSR, Nazis. You'll meet the same fate as everyone else who tried to kill us:

https://medium.com/lessons-from-history/anti-zionist-your-societys-fate-is-4a519752c67a

Here's what explains every Jewish holiday: "They tried to kill us, we survived, let's eat."

Still sure you want to become the content of another Jewish holiday?