Usually when we want things from others, we ask for those things, and we explain why we want them. But, for rights, we don't have to explain anything.
We can say that all Americans should have certain benefits, and we can argue as strongly as possible that the government should provide those certain, very important benefits. But to say that those benefits are rights is sloppy and lazy and just plain incorrect...it is a way to avoid having to have a discussion about the cost vs. benefit of the issue. This concept that I can demand something from you as a right as long as I use the force of government to do it is a very new concept developed by the Left so as to avoid discussing the merits of their many proposals for government takeover of services traditionally provided in the private sector. Every time you do this, you dilute and diminish the concept of rights.
But, if we go by your definition of rights, then by your rules, I guess if gun ownership is a right, then the government should provide a gun to every adult.