I think there are two main factors at play in most of the critiques I hear:
1) It's not a simple discipline, so at first exposure to the theory, people often respond thusly: "Huh?" It seems to be a natural human response to have some level of distrust for the unknown. Elliott Wave Theory is an unknown to most, so they reflexively distrust it.
2) People often assume that, in order to be an Elliott Wave theorist, you must somehow be tied to Robert Prechter.
As a result of these misconceptions (and several others), I have taken it upon myself to address some of the more common objections I've encountered. I've set this up in an easy-to-follow Objection/Answer format, so without further ado, let's get to the objections:
1) Objection: "I've heard at least 10 different interpretations of this market from 10 different Elliott pros."
Answer: Sometimes Elliotticians agree, sometimes they disagree. Is this different from any other form of market analysis? Turn on CNBC at any given moment, and you'll see some analysts who are bullish, some who are bearish, and some who are neutral -- even if they all practice the same discipline. Folks who chart based on traditional technical analysis are often in disagreement over the market's future. The same goes for fundamental analysis. The same goes for Elliott Wave.
Just because I practice Elliott Wave doesn't mean I'm required to agree with Joe Baggawavetheory, simply because he also calls himself an Elliott Wave Theorist. If there was any system which was so foolproof that it was always correct, no interpretation required, we'd all be using it. And we'd all have long-since retired to our own private islands to spend our days lounging on the beach while roasting wild boar over smoldering piles of hundred dollar bills.
2) Objection: "Robert Prechter! Blahblahblah!"
Answer: It is not a requirement that you be a Robert Prechter fan to practice Elliott Wave. There's a reason it's not called "Prechter Wave Theory"; the theory is actually named after its discoverer: Ralph Nelson Elliott. Some Elliotticians (myself included) feel they owe Prechter some gratitude for introducing them to the theory through his Wave Principle book... but that's about the extent of it.
Personally, I couldn't tell you if Prechter's charts agree or disagree with mine; nor do I care. I have nothing against Prechter, and as I said, I feel indebted to him for calling my attention to the theory -- but I have never been particularly impressed by his ability to actually apply the theory. I respect the guy for his contributions, but Elliotticians are not required to join some Prechter-based cult following.
3) Objection: "(Insert really well-reasoned objection, possibly containing a bunch of Latin words, which basically argues that the future is simply unknowable due to a preponderance of variables. Add exclamation points as needed, which, with some imagination, seem to be dripping with spittle)!!!"
Answer: Yes, future news is theoretically unknowable. Yet, as any good technical analyst will tell you, the charts often seem to lead the news. Is there a logical explanation for this? Perhaps. Maybe a stock is due to release a really bad earnings report next quarter. Some folks at the company know this, so these insiders start dumping the stock; then the people who watch the insiders start dumping the stock; then the people who watch the people who watch the insiders start dumping the stock; and so on, ad infinitum. Suddenly, the stock is down 30%... months ahead of the bad news, which "nobody" knew about.
Further, stock prices are based on supply and demand; and demand is always dictated by the herd. Herds often act in more predicatable ways than individuals do. Run into a crowded theater and yell, "Fire!" and people will uniformly stampede for the exits (note: I am not suggesting you try this). Run into a room where one guy is sitting and watching TV, and yell, "Fire!" and maybe the guy runs for the door, or maybe he laughs at you... or maybe he punches you. Individuals acting alone are vastly more unpredictable than are a group of people competing over the same resources. Every technical analyst, Elliott Wave or otherwise, accepts the presupposition that people acting as a herd tend to follow repeating, and predictable, patterns.
4) Objection: "I remember this Elliott Wave guy, and he predicted that the market would (crash/skyrocket) and it (skyrocketed/crashed) instead! So THERE."
Answer: Really? This critique goes back to the assumption that Elliott Wave is somehow not open to the same level of interpretation that every single other analytical tool on the planet is open to. Sometimes you just don't have enough information; other times you misread the information you have. Just because the guy was wrong doesn't mean the theory is broken. Heck, I've been wrong too. And I'd be willing to bet: so have you.
Sometimes you apply your best analysis to something, and you still just fall flat on your face. Anyone who's married knows this is true. How many times have you tried to reason out exactly how your wife will respond to something? Then after you think you've got it all figured out, you finally approach her with it... and then, despite your best analysis, you're still absolutely shocked when she gets angry that you bought a new Cadillac without so much as calling her first (note: not that I'm speaking from personal experience or anything). Hey, that's life!
5) Objection: "Why do we have hot water heaters, when 'hot' water doesn't need to be heated?"
Answer: I have no explanation for this. Also, this forum is supposed to be for objections to Elliott Wave Theory.
Objection: "Oh, whoops. Sorry."
6) Objection: "I was following this Elliott guy, and he completely changed his count! For a while, he was predicting a new bull market -- but then suddenly he said something about the fifth wave, and the third of a fourth or something, I don't know, I thought he was talking about socket sizes or wrenches. Anyway, then he started predicting a bear market! If the theory's so good, how come he was so far off?"
Answer: Well, first off: good for him for recognizing the situation had changed. There are always numerous possibilities. What good Elliott theorists do is parse the information available to them; then they decide on the count they view as the most probable, based on their analysis (they call this count their "preferred" count). But it's rarely clear-cut, and the market doesn't always tip its hand in advance. Just as a traditional technical analyst might project a target from a head and shoulders breakdown, then recant that target when the price whipsaws, Elliott technicians must do the same with our patterns. The main difference with Elliott is the patterns are quite a bit more complicated and sometimes harder to explain to a non-Elliott theorist in ten seconds.
My theory, let's call it the "Theory of Why Some People Distrust Elliott Wave Theory Theory" (I threw in an extra "theory" just to be safe) is simple: Elliott Wave seems like such an esoteric and strange discipline that certain "skeptic" personalities reflexively seek to attack and disprove it. Nothing wrong with that, I suppose. To each his own; live and let live and all that.
So, in conclusion: best of luck to the skeptics in their chosen disciplines.
Beyond that, if there are other common objections I missed, feel free to post them in the comments. :)