> 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.

> 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

Because the EU passed a law making it illegal and the temporary exemption recently expired.

Moderation is when others remove publicly posted content because you don't want to see it. (Censorship is when others remove publicly posted content because they don't want you to see it.) You don't need moderation for your private communication.

Why should you have any right to look through everyone's private communications? Nobody really has any choice to reject your EULA if they want to stay in contact with someone on your service. I could force you to sign a ToS that includes "By using our service you owe us $10 million and agree to donate your kidney to our CEO" in order to reach your overseas grandma, but that doesn't mean it's actually enforceable or legal...

the opposite question - why is it legal and was made legal?

it's unconstitutional in most places to read letters - same thing should be applied to other form of communication as well

> It would make moderation impossible otherwise.

Why would you need to moderate private messages between users?