From The Federalist Papers:

The point is that in a political and cultural environment that is increasingly hostile to the Second Amendment and law-abiding gun owners, telling anyone outside your immediate family that you are armed is a risk. It’s a risk because that information will go on your medical record and if they don’t already, the feds will soon have access to all your medical records.
And it’s only a small step until one day when liberals control all the levers of government and can impose mandatory gun registration or confiscation.