Don't you like to know that the next time you board an airplane that the pilot and copilot have had training?
Don't you like to know your doctor has had proper training when prescribing medicine to you?
Do you want anyone to be driving a car next to you regardless of his or her age or ability to drive?
Yes, we demand aptitude for things but these will not guarantee safety.
What about the pilots who are qualified ... and deliberately fly their planes into buildings or mountains or into the sea, or the qualified engineers who design a plane that crashes for them?
Doctors are great aren't they, it's a pity that medical errors and malpractice are one of the leading causes of death and over-prescribing has led to addiction, misery and death of many in their 'care'.
Everyone on the road has passed a test to deem them worthy of the license to operate an automobile, yet so many crash ...
The point is that even with background checks, there are going to be people who flip and go on shooting sprees. Background checks are a point-in-time evaluation - someone could have been fine when they got their gun, 2 years ago, and then their life changes.
It alters the probability, that is all.