-는 거 packages an activity and 싫어하다 says someone dislikes it: 아침에 일찍 일어나는 거 싫어해요 (I hate getting up early), 지는 거 싫어하세요? (do you hate losing?). Note the choice of verb: 싫어하다 describes anybody's dislike, which is why it works about other people and in questions, while the adjective 싫다 can only report how the speaker feels.