Now let's ask another question: a possible perp is arrested, printed, and later released for insufficient evidence. Later he rapes and kills someone in your family.
A DNA sample is finally taken, and he's linked to other rapes that occurred before his arrest and release. Had that information been available earlier, he'd never have been released, and your family member would still be alive.
Will the life of your family member be worth the privacy concerns you've expressed?
Of course not. But the perp wasn't released in the first instance because the State lacked his DNA samples. He was released for insufficient evidence. That's a failure of Law Enforcement. It has happened, does happen and always will happen. It may suck sometimes but that is the way the Law works in this nation. Innocent until proven guilty.
Secondly, the likelyhood of your scenario happening to me is a billion to one chance when compared to the odds of my insurance company getting the information from the gubmint's DNA database and restructuring my premiums based on what that info reveals.
Now let's ask another question: Are you willing to pay higher premiums for insurance because your supposedly private DNA submission was found to reveal a family history of diabetes?
I hate to use the tired old phrase...but having everyone submit to to giving DNA samples to The State is a slippery slope that we dare not venture onto. I have an inexhaustible faith in the darker side of human nature and Man's ability to corrupt and pervert just about anything he lays his hands on.