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

Not all services should be treated equally. We've figured this out earlier about letters, it's typically illegal, even for postal services, to open and read your letters without your consent, because there is an expectation about privacy.

Fast forward some years since then, and now basically IMs are the new letters, and sadly we have few big actors (yet again) controlling the transportation of our communication. People generally still want privacy in their communications, so regulations were made that companies cannot open your messages ("letters") without your consent, so we humans still have more or less the same protections as before, just tailored to the new specific implementation.