싫어: you don't like something; you reject something as a natural reaction. 미워: you resent or hate something actively. (generally only used for people) - 나는 이런 음식은 싫어: I don't like this kind of food. (can't use 미워) - 나는 나를 조롱하는 친구들이 미웠다: I resented [hated] the friends who taunted me.

This question was tough to me. '싫어' and '미워' have very similar meaning. Generally, When you hate 'someone', use '미워' When you hate 'someone' or 'something', use '싫어'