Mandatory firearms training does not violate one's right to bear arms. Along with our rights is a responsibility and duty to exercise said right in a manner that does not expose others to danger.
Anybody can buy an airplane, but they need education in safe operation. Otherwise, you could crash, killing yourself and who knows how many others.
Anybody can buy a car, but they have to be educated in how to operate it safely. Otherwise, you could kill yourself and your passengers, or a pedestrian, or someone in another vehicle.
Anybody can buy a chain saw, but should be instructed in its safe use. This isn't mandatory, but common sense dictates knowing how to use it properly, lest you cut your leg off because you are careless and didn't have the proper knowledge.
Guns are no different. Even proper education does not guarantee safety, or less intent to misuse one, but to do less is even more irresponsible.