Difference between 싫어요 하고 싫어해요?
if you say something is bad, you're implying it's your opinion. 이것이 싫어. This is bad.
이것을 싫어해 is more I don't like it.
As you can see, they are often interchangeable
They are only interchangeable when you are referring to yourself. If you are speaking for someone else, like in this sentence, you have to use 싫어하다.
싫다 is a descriptive verb meaning "to be distasteful, hated" while 싫어하다 is a verb meaning "to hate, dislike".
It can help to see the latter as a compound verb: 싫다 + 하다, roughly meaning "to act as if something is distasteful".