Some children with ADHD feign aloofness or shirk responsibility as a way to avoid having to face up to the rather chronic impulsive acts they commit. Saying "I don't care" may be an attempt to devalue the negative act after it has been completed. To care about what you do carries with it the implication that you will do something about it if you make a mistake. And if you make a lot of mistakes, doing something about it is hard work. This is a cycle that can be broken by responding: "You say (or act like) you don't care; but that's unacceptable in this classroom (or family). You must do something to make amends for what you have done" (and saying a hollow "I'm sorry" doesn't cut it -- the key is action).
We worry a lot about kids who do things to other people or who don't do things for other people without caring about it. The longer this behavior persists, the less likely it is that it will improve. Taking the steps outlined above will help most children become more caring and thoughtful individuals. Unfortunately, there are some children who have flawed personalities; they lack the capacity to care. This is a fairly rare, but serious condition that should be addressed in therapy.