How does my status as an armed citizen make me different from any other citizen in terms of responsibilities?
As an armed citizen you must give up certain conduct because of the repercussions involved. You can no longer engage in behavior that would escalate a conflict. You have to be able to turn away from unacceptable behavior in others. No more standing your ground if some drunk insults you, no more returning the middle finger salute when a driver cuts you off in traffic.
Basically you can't escalate. The possible consequences if you do while you are armed are just too great.
You don't have any responsibility to protect the public, you have no duty to act. A CCW permit is not a peace officer's commission. It allows you to carry a weapon to protect yourself and your loved ones, not the public at large.