What the E-2 rule actually says
South Korea's E-2 (Foreign Language Instructor) visa, used for both EPIK public-school placements and private hagwon jobs, is restricted by law to citizens of seven countries: the United States, United Kingdom, Canada, Australia, New Zealand, Ireland and South Africa. This is written into immigration policy, not left to individual employer discretion, so a hagwon that wants to hire you still cannot get an E-2 approved for a passport outside that list.
This is one of the most rigid passport restrictions in the industry — stricter in practice than Vietnam or Thailand, and similar in spirit to Japan's Instructor visa rules but with a shorter, explicitly named list rather than a broader native-speaker/English-education test.
