I have several reasons for not letting an LEO check my ID:
1) As has already been stated, a cop needs to have RAS that I have committed or am about to commit a crime. In my home state and elsewhere, it has been stated by multiple courts that a properly holstered and visible weapon is NOT RAS of a crime; further evidence is needed before you are required to provide ID. Simply saying or doing nothing is the easiest thing to do, but you can always say "I would like to speak with a lawyer," or "I do not consent." I have also heard a tactic is to answer their question with a question, like: "What probable cause do you have?"
2) Anything you say can and will be used against you in a court of law - there is always the possibility you may accidentally incriminate yourself, be mistaken for someone else, or say or do something that can lead to arrest and forfeiture of your firearm. Play it safe and do not say or provide anything.
3) It is not about having anything to hide, it is about having everything to lose - the police are not there to help or protect you. They are there to find evidence of criminal activity and arrest you if they find something. There are two parts to this IMO - You may unintentionally be hiding evidence of criminal activity (somebody might put drugs somewhere in your car, in your home, or on your person - not to mention somebody in your company may have something too) and like point (2) ANYTHING you say WILL be used against you. Nothing you say will help you. Second, it is your right to not say anything as well as be protected from unreasonable search and seizure - and like point (1), the courts have ruled that merely having a weapon does not constitute being unreasonable and therefore the 4A and 5A apply and it is up to YOU to enforce it.
4) Cops are allowed to lie and make threats - or scare you into compliance. Personally I find this distasteful and immoral and will stand my ground and not let them intimidate me.
It is our duty as citizens to ensure that those appointed in authority over us remain within their authorized limits. If you let them use inappropriate authority, they will continue to push the boundary of those limits. Our Republic can only function as long as We The People enforce those limits.
If I am merely walking down the street the above applies - if I am pulled over, my response will depend on a few variables. If they ask if I am carrying, I personally do not want to lie. I would also reveal the location of a weapon if any lawful orders from the officer require that I have to go near my weapon. Such action would be for my safety as moving towards a weapon without the officer being aware of it would probably lead to some form of unpleasantness.
A large part of how a cop responds to you will depend on your attitude. Showing utter contempt will get you nowhere - there is a place and time to lodge complaints if their authority is overstepped and outright resistance will probably end very badly for you. You can assert your rights without being a jerk about it.
