There's nothing more classic than the five-paragraph essay. They're what people think of when they hear the word: an introduction, a thesis, three body paragraphs, a conclusion, and a bibliography. Everyone has written some in high school before, so they must be the pinnacle of persuasive writing, right? Nope. In fact, I'd go so far as to say that five-paragraph essays are bullshit. They're rigid, they're stifling, and they're too focused on formality to really get their points across. Let's examine.
First, look at the classical essayists such as Francis Bacon. Bacon is usually seen as the "father of essays", but none of his works even come close to fitting the modern idea of a five-paragraph essay. You could argue that his essays were simply in a different style, which is true, but that's hardly honest. When people hear the word "essay", the only thing they think of is the five-paragraph format. Most people don't actually know the real meaning of the word. Granted, the five-paragraph format can be a bit flexible -- I have been asked to write seven-paragraph essays in the past -- but it is always held to the same standards of rigidly-defined structure. Structuring essays in this way will often make them worse. The writer might have more to say than the template allows, or they might have less. A short essay can be every bit as meaningful as a long essay, but the five-paragraph format discourages essays below a certain length.
On top of that, the limits of formality often cause the writers to be verbose. Brevity is one of the defining features of an essay (with a few notable exceptions), but the requirement to be "formal" in the academic style tends to balloon the word count without ballooning the actual content. An essay I wrote in my free time last week was only 614 words long. Shortly after writing it, I was assigned something in school that allowed me to reuse the ideas from that essay. No problem, except that I needed to rewrite it to fit the five-paragraph format. This included adding a weak third point (since the original only had two points), and repeating myself several times in order to accommodate the thesis, introduction, summary sentence, etc. The essay that I ended up handing in had increased from 614 words to almost 1100 words, and it was actually worse thanks to the unnecessary third point and the stifling formal style. I had to replace every instance of generic you with the word "one", which resulted in the most hilariously stilted conclusion I've ever written. I also had to remove all references to myself -- the idea being that I would replace it with an external source -- but since I'd written the essay from my personal experiences, this ended up making the entire thing into an incoherent mess.
Five-paragraph essays still have meaning, of course. A lot of them can be great reading. I just think they do more harm than good when taken past what they're good at. What they're good at is teaching people; they're just a learning tool for people to learn the basics of argumentative writing. Once you know how to argue a point in writing – analogies and repetition being good starting points -- the five-paragraph template becomes a crutch. Truly great writers are flexible, and they experiment with their writing for the best effect. There are better things out there than a format so stifled that you can't even use the word "bullshit". Isn't that a great word to use in an essay? It certainly sums up my feelings.
I'm being facetious in the details, obviously. Gratuitous swearing and sarcasm are good things to forbid in an academic context, and avoiding "personal essays" is probably best if the writer is still in school. But for every good thing about the format, there's one more "oneself", and one more I-statement awkwardly rewritten to use a different person. The five-paragraph essay prescribes to silly -- and sometimes completely arbitrary -- restrictions, and that doesn't make it a good format for people to think of when they hear the word "essay". It stains the name of a great genre of writing.