apathy is a response, to keep one's sanity. i don't think anybody chooses apathy at the outset. when faced with a concern, the normal thing to do is do something about it. but sometimes the concern/issue seems to great to even attempt to start addressing it. this is when the mind opts to label the concern as a "non-concern". when one finds in him/herself a lack, whether in terms of skill, talent, means, resources, etc, to fight, many people often take the easier route. that is to say that "this issue doesn't concern me at all". in that way, he keeps him/herself from the anguish of not being able to do anything, and in the process keep his sanity intact.
therefore, i think that one way of addressing apathy is to make people aware that they can do something about a particular concern, to make them see the value of not easily giving up. putting emphasis on the value of little contributions to fighting against a big problem is one way. another way is to show that a big problem manifests itself in smaller places, where definitely, one's little actions can have bigger chances of success.