It has nothing to do with music. The sharing of music is only a side-effect of free and private sharing of digital information in general.
There are a number of drawbacks with enabling private digital communications: It makes the sharing of copyrighted works possible without the possibility for law enforcement to intervene, it enables the spread of child pornography or other criminal and morally unjustifiable information, etc.
The thing is, that is a price that is worth paying, because the alternative is a complete loss of liberty. If the government can prevent you from sharing music, it can prevent you from sharing anything. This may not be a problem for you personally right now, but it is a huge problem for people living in North Korea or Syria, for example.
Besides this, it is not at all clear that private sharing of digital information is automatically detrimental to musicians. While it is easier to share music for free, it is also easier for the musicians themselves to reach out directly to their fans. Whereas it used to be the case that you needed a record deal signed with a major label to have anyone even hear your music, these days you can become a major star, making a comfortable living off your music without ever signing a contract with a major label.