Why my iPhone says remanufactured by asurion?

I've never heard of "remanufactured". What's wrong with refurbished?

A quick search found that Asurion is a company that provides insurance for various smartphones and electronics in the United States. It's likely that they acquire tech (including iPhones) as part of an insurance claim; the claimant gets the cash while the company gets the item which then goes into their warehouse. From there it would follow that it is used as spare parts to bring another unit up to spec for sale as a legitimate repaired item, it would seem with their name on it as advertising.

Did you acquire yours as a used item?

The first letter in the model number represents the source of the device. Currently, there are four known possible choices:

• "F": refurbished unit
• "M": retail unit
• "N": replacement unit
• "P": personalized (engraved) unit