While I strongly advocate that any firearms owner should seek and learn about the proper handeling of a firearm, I cannot endorse forcing it upon them.
Ultimately, the way I look at it is that an irresponsible individual is going to be irresponsible regardless of the what he or she has been taught. There is no gurantee that forcing firearms education upon the masses will reduce tragedies.
Someone who respects the firearm and is willing to spend just ten minutes on YouTube will have already done so as it is. It's like telling your child something is wrong and they shouldn't do something, but in the end, it's their decision to carry out whatever that something is even if they know it's wrong.
Morality and self accountability is something you cannot legislate no matter how much you try or wish that you could.