Legal definitions are often not the same as plain English, and wording used in legislation is often politicised.
The nature of copyright is that it is a monopoly right. It is almost indistinguishable from letters patent (e.g. in the case of the KJV Bible in the UK). I am less familiar with US law but I believe US copyright law is based on a clause in the constitution giving the federal government the power to grant monopolies?
A monopoly right and a property right are the same thing with different names. As a landowner, for example, you have the right to kick people off (evict from) your property. You have both a de facto and de jure monopoly to exploit your land.
The US constitution confers to Congress the power to grant copyrights and patents in Article I, Section 8:
"The Congress shall have Power ... To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries"
The operating word here is "exclusive" which, yes, is a monopoly right. But again, it's not different in essence from a property right, which is also a monopoly right.
The nature of copyright is that it is a monopoly right. It is almost indistinguishable from letters patent (e.g. in the case of the KJV Bible in the UK). I am less familiar with US law but I believe US copyright law is based on a clause in the constitution giving the federal government the power to grant monopolies?