"They hated him because he was Assyrian"

Heller cannily assigned his hero a nonexistent ethnicity (or rather, one that is ancient and of uncertain historic validity today). At various times they have been known as Assyrians, Chaldeans, Syriacs, or Syriac Christians.

Assyria was a Middle Eastern kingdom named after its capital, the ancient city of Assur, centered on the Upper Tigris River where Persia and eventually Iraq would later be situated. The three primary periods of Assyrian ascendancy lasted from the 20th century BCE to the mid sixth century BCE, after which the neo-Babylonian, Median, Parthian, Roman, and Persian empires took over in turn.

Assyria (indicated with gray outline as
Creative Commons Attribution Share AlikeAssyria (indicated with gray outline as "Assur") during the Amarna period

It’s also an appropriate ethnic background for Yossarian because the Assyrians have a long history of being persecuted minorities, often driven from their homes by other peoples. Many emigrated to the Caucasus, Europe, and North America in recent centuries, or were periodically massacred (for example, by the Turks in 1914-20, and by the Iraqi government in 1933 and 1979).

The whole notion that the other men in his squadron would hate Yossarian "because he was Assyrian" is laughable, because they wouldn't know what that was.

In Closing Time, the sequel to Catch-22 that Heller published in 1994, Yossarian is said to be an actual Armenian (the name resembles one from that ethnic background) posing as an Assyrian.