This is apathy - the opposite of empathy.

An apathetic person would be inclined to shrug their shoulders and walk away from a situation not directly involving themselves. It is a 'Why bother, not my problem" sort of thinking pattern. An empathetic person on the other had is likely to be deeply affected by a difficult or painful situation another is feeling and have an inclination to want to get inovlved. They see some one else's problems often as their own.

A big example right now is the current gun debate.