"Qualify" is correct. Because you would need to say "He is not fit to be an English teacher" if if the correct answer was "Fit" Though in this case they both have nearly the same meaning.... "Fit" can imply that even if the person is qualified to be an English teacher, they are not a good choice for whichever reasons. For example: He is qualified to teach English, but he conducts himself in an inappropriate manner, there making him unfit for the position. Hope this helps you!