My ER doctor friend says urban cycling is idiotic.A friend of yours said something, so it must be true...
Most accidents are due to people driving their bicycles unsafely. If you drive safely, urban cycling is not dangerous. If you drive like a maniac and disregard traffic controls (running lights, riding on the sidewalk, going the wrong direction, etc.), then yeah... it's dangerous. Just like it would be as a pedestrian or motorist.
In aggregate, cycling is not significantly more dangerous than any other activity: http://bicycleuniverse.info/transpo/almanac-safety.html
(Despite this, I am in favor of laws and regulations that make the roads less dangerous. Cars should not go faster than bicycles in cities. If you need to get somewhere fast, use rapid transit.)