Until recently, I lived in the Springs for over 9 years, the traffic situation there is horrible, and it's only getting worse as more people move/are stationed there. Traffic can be a serious source of aggravation for plenty of people, especially when there are no quick routes anywhere. Time is precious to everyone, so the sense of futility that your time is being wasted dealing with other drivers or traffic jams is infuriating. Sadly, riding in the city isn't that much better. Yes, you can get around a bit faster, but at a highly compounded risk. Needless to say, if you find yourself raging in a car, it won't be long before you're kicking doors or smashing mirrors when drivers pull boneheaded maneuvers around you. The reason being that on a bike you are vastly more exposed to danger, and whereas in a car it might be a fender bender, on a bike it can literally be life or death. Ask yourself, do you really think, given the anxiety you experience in a car, that it won't bleed over on a bike?
The solution, I'm afraid, isn't changing your mode of transportation, but, as has already been said, by changing your state of mind about it. When those situations arise, the best advice I can give is to remind yourself that worrying about things you can't control is like needlessly carrying the weight of others' poor decisions. It's not easy and takes work, but, in the end, you will lift yourself above those problems and find that you can be easy going in the car just as you are everywhere else.