If you're unconcerned, you don't care — you're just not that interested. It's not ideal for the principal of a high school to be unconcerned about bullying.
It can hurt your feelings when you sense that someone's unconcerned about your well being or happiness. A soccer coach might appear to be unconcerned about her players if she yells at them to get up and keep running whenever they fall and hurt themselves. The word can sometimes have a less callous meaning, when you're simply not worried about something: "I'm unconcerned about my SAT score — I'm sure I did fine."