There is a third party involved in that decision
There is no one "reading your mail", so to say. What goes on is someone seeds a torrent or otherwise uploads infringing content and the RIAA/other party sees a list of IP addresses that are seeding/uploading that content and subpoenas someone so that from there on their traffic is monitored by their ISP to look for further traces of infringing content.
Under the Fourth Amendment of the Constitution of the United States, their traffic is subject to search and seizure (seizure being the termination of Internet service due to violation of the provider's Terms of Service) because that uploader has broken the law. The ISP should be the one who sees the warrant to search your traffic since your unaltered traffic goes through them. Whether this is reasonable or not can be questionable, since you, the violating party, doesn't see any documentation of what is happening until you get a Cease & Desist notification in your inbox.
Short version: your traffic is not monitored without good reason.