I learned it first in high school (1987 or so), and then again in much more detail in college at the University of Chicago, in the excellent "Little Red Schoolhouse" course on composition (along with learning thesis statements, topic sentences, smooth transitions, and more advanced rhetorical techniques). I teach the five-paragraph essay now myself, in both basic and more advanced form, to my composition students.
The very basic idea is this:
- given that you want an introduction and a conclusion
- and that as a minimum, for any argument, you want three supporting points (once is an anecdote, twice is coincidence, thrice is the beginnings of actual evidence)
...it then makes reasonable sense that the minimum for a basic essay should have the following:
- intro paragraph
- paragraph of support
- second paragraph of support
- third paragraph of support
So especially when you're introducing under-prepared students to the essay form, the five-paragraph essay is a helpful starting point. It gives them a structure that they can use for their initial short papers, and breaks down into comprehensible segments ( at least three pieces of evidence + analysis within each paragraph supporting the paragraph's main point, for example). It also expands well to longer essays -- the three paragraphs become three (or more) sections, of whatever length and depth necessary.
In my more advanced composition classes we study other rhetorical structures, and discuss some of the weaknesses of the five-paragraph form. For example, there are huge cultural aspects to essay writing; in standard Japanese composition, for example, one would likely never state one's main thesis point, since the reader is meant to understand it by implication; it would be insulting to state it out loud. As opposed to the American standard form, where we tell you three times, and a few more times just in case you didn't get it already. The Latin American forms tend to be much more digressive. The Chinese forms are more likely to rely on evidence-by-expert witness, as opposed to evidence-by-broad study. The Arabic forms have been known to rely on evidence-by-beauty, which I find personally rather appealling, but is a technique I wouldn't recommend for my beginning students.
My point is, there's nothing inherently wrong with the five-paragraph-essay. It's a useful technique, especially for underprepared beginners, and has utility beyond the beginner level. The problem is that so many people teach it in a rote manner, without explaining why we use it, what its strengths and weaknesses are, and what some of the other options are for the more advanced writer.