I live in EASA-land (Europe), here we call our flight instructors simply that, "FIs". That they hold an instructors certificate is simply implied. Why are flight instructors in FAA-land (US) called CFIs? Is there any historical reason why the "C" is always added to the abbreviation, e.g. in the past there was a difference between certified and non-certified FIs (if there ever was such a thing)?
Certified flight instructor = CFI. Add a multiengine rating to your CFI and now you are a multiengine flight instructor, or MEI. An instructor with single and multiengine instructor ratings is commonly referred to as a CFI/MEI. What if you are a CFI but only in gliders? CFI-G is the most common shorthand.
Pilot authorizations are specifically called "certifications" in the US, not "licenses." My guess at the inclusion for the C in CFI is that any pilot can provide instruction but only appropriately certified and rated instructors can provide training that can be counted for a student's training for a new certification, flight review, or whatever.
Actually, in the US, the accepted term for a flight instructor by the FAA and the general aviation (not to be confused with General Aviation) public is Certificated Flight Instructor (CFI). An instructor for instrument ratings is called a Certificated Flight Instructor-Instrument (CFII). This is opposed to a Basic Ground Instructor (BGI) or an Advanced Ground Instructor (AGI).
Although these terms are not defined in Title 14 of the Code of Federal Regulations governing aviation, they are used extensively thought out this document. So is the term authorized flight instructor (which is defined). People may have simply followed the lead of the predominant legal authority.