I will try to answer, based on what I've learned :) 안 좋아해요 (안 ~다) is the short form of 좋아하지 않아요 (~지 않다). Both express negation, but the long form is frequently used in writing, and it is used when seeking agreement from the listener. (어렵지 않아요?) The structure is like ~지 못하다 and its short form 못 ~다 ("cannot").

i think same case with dont and do not? i cant explanin the grammar but my korean language teacher said so though shes not korean..