It is because expressions describing emotion or state of mind have two forms. For the first person "I", you use the adjective form (나는 슬프다, "I am sad"), while for the second and third person, you use the corresponding verb with the -아/어/여하다 ending (그는 슬퍼한다, "He feels sad"). This is an established way that applies to present tense simple sentences (i.e. reported speech and conjectures ending in -나 보다 or -는/인 모양이다, etc. can get around this rule). It makes the first person expressions more direct and forceful. For example, - 나는 즐겁다 / 그 사람은 즐거워한다. (즐겁다, 즐거워하다) - 나는 비 오는 날이 싫다 / 동생은 비 오는 날을 싫어한다. (싫다, 싫어하다) - 나는 누가 이겼는지 궁금하다 / 친구는 누가 이겼는지 궁금해한다. (궁금하다, 궁금해하다) '해하다" arises from adjectives ending with -하다(e.g. 섭섭하다): 섭섭하다 + -아/어/여하다 -> 섭섭하여하다 -> 섭섭해하다. Having two 하다 form is just a coincidence - there is nothing special about it. For certain words (e.g. 좋다, 싫다, 밉다), the first person sentence can take both forms, with a slightly different connotation. - 나는 저 사람이 좋다/싫다 = can mean a spontaneous emotion of the moment or existing preference. - 나는 저 사람을 좋아한다/싫어한다 = always an existing preference or dislike. In most cases though, the -아/어/여하다 form sounds strange for the first person (and using the adjective form for non-first person is even worse). - 나는 행복해한다 - UNNATURAL. - 동생은 불고기가 좋다 - BAD => 동생은 불고기를 좋아한다.

For certain adjectives, when someone looks to you like he is experiencing certain emotion, you can describe how he is feeling by adding a 아/어/여하다. The grammar rule is A-아/어/여하다. I believe it's a level 2 or 3 grammar rule. ps: A proper answer should come along in time.