The song is about empathy and purpose which shows through various lyrics through the song. The "Leave me alone" and "Go away" parts I think mean he wants to be left alone to his own thoughts and be his own "shrink" which is also a lyric. He doesn't want to share his thought with others because he feels it would lose purpose. This song may just be about a simple kitchen sink to you but to him it means something really important.
"At my kitchen sink. You don't know what that means. Because a kitchen sink to you, is not a kitchen sink to me."
Give kitchen sink a listen and give me your thoughts and theories on it!