From The New Oxford American Dictionary
1.-- noun, the state of not being influenced by personal involvement in something; impartiality: I do not claim any scholarly disinterest with this book.
2.-- noun, lack of interest in something: he chided Dennis for his disinterest in anything that is not his own idea.
1.-- verb, feel distaste for or hostility toward: he was not distressed by the death of a man he had always disliked.
2.-- noun, (a) feeling of distaste or hostility: despite her dislike of publicity, she was quite a celebrated figure | they had taken a dislike to each other., (b) a thing to which one feels aversion: I know all his likes and dislikes.
When discussing an issue, always remember the two and never think a person's disinterest is dislike. When someone says, "I don't care about ...", it may be that they don't really care one way or the other about it, and not have a dislike for it.