I never did see anywhere in the Constitution where any government has the right to dictate what people's rights are and are not.
The Bill of Rights simply enumerates, i.e. names and numbers, a set of rights that the government is specifically enjoined from infringing. It does not grant you rights.
However, anyone who violates the laws of the land may be stripped of SOME rights,
through due process of law. To deny that would be to say that, just because someone is murdering his neighbors, he can't be denied the right to freedom, weapons, and the pursuit of happiness (or even life in some states).
Which actions are crimes and which crimes require the removal of which rights -- once due process has been seen to -- are matters for legislatures to decide. Not the Constitution and not the Executive or Judicial branches of government.
People are right about one thing - all the government has to do is make something a felony or in some cases an unrelated crime to revoke inalienable rights.
I don't know which people ever said that, or why saying that would make them "right" but -- in a government of the people, by the people, a system of laws is established. Once established, individuals BREAKING those laws subject themselves to the possibility of having some of their rights removed (some temporarily, some permanently) as society applies the due process of law against those individuals in court.
Even felons and mentally ill people, according to the constitution, have the right to keep and bear arms.
I don't think you understand the concept very well. Rights CAN be removed through due process of law. That's an utterly necessary function of a justice system. Putting someone in jail is a removal of their rights. Executing a convicted murderer is a removal of their MOST FUNDAMENTAL right. Yet, it must be so.
How about this: instead of keeping guns away from bad people, how about keeping bad people away from guns?
Oh...but I thought you couldn't deprive someone of their rights, under the Constitution?