> If I have a service that let's users communicate, why is it illegal to look through those communications?

Because of https://en.wikipedia.org/wiki/Secrecy_of_correspondence

It guarantees that the content of sealed letters is never revealed, and that letters in transit are not opened by government officials, or any other third party. The right of privacy to one's own letters is the main legal basis for the assumption of privacy of correspondence. The principle has been naturally extended to other forms of communication, including telephony and electronic communications on the Internet, as the constitutional guarantees are generally thought to also cover these forms of communication