In order to obtain a work permit in another country, a university degree is required unless you are a citizen of that country. The degree does not have to be on education, TESOL, or anything related to teaching. In fact, most TESOL trainees have degrees in business, history, and art.
Having a degree in an unrelated area does not indicate that the applicant can teach English. The reason immigration offices require a university degree is to avoid young backpackers who are usually irresponsible with their students, their contracts, and used wreak havoc when there were less restrictions. Gone are the days when any native-speaker could move to another country and find a job teaching English. Language institutes have established a professional industry in which a degree and an internationally recognized TESOL certification are required.