To clarify, it's not a monopoly and copyright was invented, as stated in the copyright law (quoting the constitution) "To promote the Progress of Science and useful Arts, by securing for limited Tımes to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." You can read the full U.S. copyright law
here and it's rather clear cut. The point of copyright is so creators are protected to receive payment for their work in order to carry on creating more works instead of people just copying their work for free. It's to support creators. The limited duration is so that the protection will expire after an adequate time to prevent monopolies from occurring. (Unfortunately Disney's lawyers keep pushing the expiration date to hold onto Mickey Mouse and continue their monopoly.)
To iterate what I've learned about copyright laws:
In
section 102 of the copyright law it states that it protects "original works of authorship fixed in any tangible medium of expression", keyword being "tangible" such as books or sheet music. The digital age resulted in more laws being passed to protect music and media stored in a digital medium. Section 102 includes a list of what types of media are protected by copyright.
Section 106 lists what exclusive rights the copyright owner has on their copyrighted work. These include the right to make copies, the right to make derivatives (the exception being what falls under parody law), the right to distribute copies either by giving, selling, or renting, the right to perform or display the work publicly, including via "digital transmission".
The question isn't really about whether you feel or believe copying/sharing music right or wrong, legally it's always wrong unless you obtain the rights to do so. Most of the time only parts of these rights are given to third parties, such as movie theaters, stores, coffee shops, etc. Buying a copy of a piece of music does not legally give you any right to those listed in section 106. If you're old enough to recall VHS tapes you might remember the "FBI Warning" at the beginning which says very plainly that even though you own the tape, you're not allowed to copy it or play it publicly.