Who owns the message? The sender or receiver? That is a question that bugs me once in a while.
If I send you an email, same thing, if it survives for such a long time. Does Google/any ISP also own it?
If I send you a SMS, same thing, I bet it won't survive. Does the phone company also own it?
If I write you on a social network, do you and I own the message or does the social network own it? There are ToS that we might not have read.
To the down-voter: could you please elaborate with what you got the problem so we could potentially discuss it?
While the receiver of a letter on paper certainly owns the letter she doesn't own its contents. The copyright of the letter remains with the author.
So you can frame the letter and hang it on your wall you violate the authors copyright if you publish it without authorization.
What you can do is sell the physical object. That belongs to you.
You can also burn it or destroy it - which is an interesting edge case.
This really comes down to different kinds of ownership. The whole point of copyright is that creative/cultural/intellectual property rights are a thing, analogous to tangible property but with a different set of legal and commercial rights and obligations.
Electronic media depend on context. ISP and telcos are usually considered common carriers so they don't own the copyright of emails or SMSs.
Social media networks either claim all copyright in full (bad news for you...) or have a specific license clause in the T&Cs which gives them reproduction rights.
Sometimes these are for specific limited purposes, and sometimes they're a blanket sign-away of all exploitation rights. (Bad news for you again.)
Also, how does it work if a whistleblower gives a journalist letters that they received from someone else? Is the journalist not allowed to publish them in an article?
i.e. John Does said, "Hello world" -> [Removed] said, "Hello world"
If I reveal I'm a criminal is it any different? What If it's 10 years later and I've served my sentence? Does it matter if the crime is morally wrong or even illegal where you live?
What it it's personal but not criminal, say I've come out as gay or a republican or a democrat or a communist.
I think we would be foolish to rely on greater privacy than is provided by terms and conditions and logically we will only acquire more favorable terms by requiring them in law. You gave a good example When you discussed being unable to delete data pertaining to your account.
I think on a one to one message your recipient has a right to a record of what you actually said I don't think allowing one side to edit it after the fact facilitates honest conversations nor does it much protect the person who reveals sensitive information to do so. You can already attest to what they revealed or keep a screenshot.
I think on a many to many forum like this thread that people ought to be able to control what new users see but people who already received the initial version have a right to the information imparted to them.
Basically I view a message as belonging to everyone who received it and the service ought to retain it as long as one person whom it belongs to wants to keep it.
I can see good reason to selectively remove content that is illegal say child or revenge porn but I feel like further restrictions ought to fall on the ethical reasoning of the receiver not technology to answer the complex moral implications.