is more than just protection. It's about the right to own guns.,
"Yes, subordinate to the right to self-defense.",
No. The right to have a gun, as long as you don't hurt anyone with it. We can sit here for hours and bicker about whether we'll have a safer, happier populace if we disallow guns all day, but the United States was founded largely on the Lockeian concept of rights, not the Principle of Utility. You have to show either (a) that we don't have the right to bear arms or (b) Utilitarianism is the way to go. And you can't prove the first using a utilitarian argument unless you also prove the second.
I'm somewhat pro-gun control, but only to a very limited extent.