No, carrying a gun does not obligate you to act on someone else's behalf. Moreover, most (if not all) states tend to follow the "American Bystander" rule for liability--namely that as a civilian you have no obligation to save another from harm, even if you are able and qualified to do so, and that your lack of action does not leave you criminally or civilly liable. You are not a police officer and your only obligation is to protect yourself from imminent bodily harm. I don't know what use of deadly force training CCW holders get in other states, but I know that if I am in a situation, on or off duty, and discharge my weapon then I had damn well better be correct in my judgement call. Whether you choose to act or not is a moral choice...just make sure that if you do choose to act you are legally justified in the actions you take. Also remember that even if you DO act in a justifiable way, you may still have to go through a trial to prove you were justified--cop or citizen, if you shoot and kill someone your case is going to go before at least a Grand Jury--this means stress, lost time and legal fees. Still better than being dead, but enough to make you want to be certain in your mind that your acts are justified first.
I am lucky to work for a department that puts us through a lot of tactical and force-on-force firearms training. Having done so, let me stress that when you decide to take on an armed BG there is a high probability of getting shot yourself. It may not be a fatal shot, but taking a round in the arm, leg or gut will HURT, may cause long term disability and will certainly take you out of work for a while--I am covered for that by my agency, are you?
While we're at it, I've seen a few posts with quotes similar to this one: "The police don't have the obligation to stop a crime in progress... Their obligation starts once the crime is commited."
Quite to the contrary, if I OBSERVE a crime in progress and I can act to prevent it without UNNECESSARILY endangering others then I am obligated to do so. What you fail to recognize, or conveniently ignore, is the difference between being obligated to and being able to do something. There are also legal restrictions of proof that we have operate under that often handcuff our ability to act BEFORE a BG makes an overt criminal act. There have been times that I have found BGs casing businesses for burglaries. I "know" what they were doing but I can't prove it and, since they weren't trespassing or doing anything else illegal, I have to let them go...we'll keep an eye out and hopefully act as a deterrent in this respect but we're not legally ALLOWED to do anything else. I don't like this part of the system any more than you do, but I have to work within the system or else I become just as bad as the BG. You're right that we CAN'T protect you from all the evils of the world, but that doesn't mean that we won't protect you when we can.
It's easy to be a hater, but if you try to understand the real world you'll see that it's not as black and white as you'd like.