From what I know, people use "for your information" for rebuttals or simply to point out the mistakes others make.

However, just from the plain definition of the words, it doesn't hold that meaning at all.

Why did people started using this phrase for this purpose? Any special origin for this phrase?
No, nothing special. That is how language evolves. Anyway, it has more to do with tone of voice, as do many other seemingly innocuous utterances: I broke the dish, did I? Really? Who told you that? I see what you're getting at. Etc, etc.
holydukefor your information
This expression can be used in a neutral way, simply suggesting that the listener may be interested in the information in question. When used sarcastically, it is meant to imply that the listener was not intelligent enough to know the information that he should have known.

holydukeWhy did people start using this phrase for this purpose? Any special origin for this phrase?
No special origin that I know of. The phrase has probably been around for centuries. There's actually nothing special about the phrase. You can deliver the same message with a variety of phrasings. For example, you might say, "It doesn't take a genius to know that ..." or "If you were better informed, you would know that ...". There is no special origin for any of these. "For your information" just happens to be a short and effective way of saying it.

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Dear Holyduke

This is just my opinion from the UK..

The expression "For your information" was probably spread by government documents that told you exactly what to do (and what not to do) in some situation..

- For your information - in the case of a nuclear attack...

I think this is what makes it sound as if you are ordering other people around; rebutting them; correcting their mistakes..

However, in emails nowadays, you can just use FYI to mean: "you might be interested to know this"

Regards, Dave
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Hi all

Just in support of my idea: the phrase echoes..

- For Your Eyes Only

This is used by one government official to another when the information is not to be passed to other people

It is of course the title of a James Bond story, when the famous spy is given information that only he may know..