I may be exaggerating a bit, but not much; every year at least one teacher gives a refrain along these lines. One year it was even the media instructor who pitched in. From a very limited, unscientific survey of nieces and nephews, it appears this is a common attitude in public schools (I don't have any nieces/nephews in private schools, so they were excluded).
I suspect there are two major prongs to this infernal pitchfork. First, Wikipedia is an encylopedia. Second, the fact it is crowdsourced.
I literally grew up with encyclopedias; we had both an Encyclopedia Brittanica (to used only with parentally-checked clean hands) and a Junior Brittanica. I never read them from cover-to-cover, a charge sometimes leveled on the playground, but I browsed the Junior volumes quite liberally, flipping through a volume until a photo, map or diagram caught my eye, or looking up one thing and then grazing on the articles on the same page. The school libraries would have a wide array of other encyclopedias -- World Book, Funk and Wagnall's and many others, but I always had a bit of bias towards Brittanica.
It is a curious thing how schools treat encyclopedias. At first, they are eager to get students to use them, given the wide array of information they contain. But soon, students are steered away to other texts. This has merit, since encyclopedia entries are so succinct and boiled down. Many topics will have a paragraph or two; only a really huge entry (such as a major war) would have multiple pages. Also, the articles aren't really much of a springboard; few if any have citations of their sources.
I fear this is the first distinction which the educational establishment has failed to realize: unlike a typical book-form encyclopedia, most Wikipedia entries contain citations against which the condensed form can be checked. Ideally, this is what would be taught - use Wikipedia, but use it carefully.
Wikipedia also is far richer than a typical encyclopedia. A few years back, the prohibition on Wikipedia was laid down for a project on the element tungsten. We found some great books on elements, but for kicks I also checked out the entry in the online Brittanica. Not surprisingly, it was very short, perhaps a paragraph or two. In contrast, the Wikipedia entry was far more detailed then about any of the printed versions we found.
The other oft-cited concern with Wikipedia is over its accuracy, given that it is compiled by volunteers rather than experts in the field. Indeed, there have been highly-publicized examples of vandalism or highly biased information in Wikipedia entries. But in my experience, this is exquisitely rare. On subjects in which I have existing knowledge I trust, I have found few if any errors in Wikipedia entries. I've cleaned up small errors, fixed verbiage and added missing material, but not once can I remember actually removing something that was incorrect. A few times I've toned something down to make it more neutral, but these cases did not contain outright errors. And again, it would be far better to train students how to verify and dig deeper, rather than enjoin them with a blanket prohibition.
Wikipedia is one of a host of amazing resources that I wish had existed when I was a kid. I often browse Wikipedia to pursue my hobby of history. I've once used a Khan Academy-style video to refresh my one-time training in 1D NMR analysis, just so I wouldn't feel so stupid when our structure determination guru was enumerating the evidence from which one of our novel molecules was divined.
The emphasis on printed materials over Wikipedia and similar resources has another flaw, which I remember from my sojourns with the family encyclopedias. One of my favorite topics in those days was the space program, but I soon learned about copyright dates and publishing lags. I think the junior set had a small entry on the first Gemini missions, and the big one might have had Shepard's flight covered. Similarly, I could see the difference between a children's globe I had acquired and the much fancier globe my father kept in my parent's room: his had many obsolete political units, as it had been drafted before the decolonization of Africa. I got another taste of this during a sixth grade debate on the feasibility of moon colonies; my "pro" team used current sources, but the "con" team dredged up all the fantasies of being swallowed by infinitely deep moon dust which had been proven false by Apollo and Surveyor and Lunokhod. They had relied on the space books in the school library, which I had long ago mentally partitioned into valuable and painfully outdated. This is one of the greatest strengths of Wikipedia, in that information in it is so rarely stale.
I've seen a particularly powerful example of how this brave new world of the Internet can be used to advance education, and for me it is even better as I get to tout the cleverness of my offspring. Two years ago, he had a project on Gothic cathedrals, which consisted of a set of specific questions to answer and also an approved list of internet sources for answering them. Naturally, Wikipedia wasn't on the approved list. Furthermore, information used in the report must be cited (the conversion of citing information from ways to verify facts to an utter fetish is a rant for another day)
After reminding him that we had actually visited Notre Dame a few years before, we first watched a video off the list, a PBS production of the David Macaulay book on castles. This was quite a good overview, but an unindexed video is a nightmare for pulling out specific, citable facts. There was also a Facts on File online entry on the list, which was useful but very limited; perhaps it would occupy two pages if printed in a reasonable font. In any case, there was nothing there to bear on some of the specific questions about specific cathedrals. Another link was to an exquisitely detailed exploration of the stained glass windows in one specific cathedral, far more apropos to a graduate student in art history and in any case no question pertained to stained glass window details nor to that cathedral. The final approved link was non-functional.
So, I cheated. With protests from the son, I started looking in Wikipedia, if for no reason than to at least know the answers he should be looking for. Perhaps we had missed them in the Facts on File, or perhaps they were in the video and would be spotted if my mind was primed. And indeed, I could very quickly find why Salisbury Cathedral had replaced the one at Old Sarum (one of the questions; if the answer was in the approved material, it was in that broken link!)
I was doing this during one of the breaks which is an agreed-on component to any large homework assignment. Normally he would go do something completely unrelated, but he started pointing out to me cathedrals he had found by searching Google Maps. My habit is to usually have only the map showing, but he likes always having the aerial photographic view open -- and he started flagging cathedrals that seemed off. Why is Chartres' roof green? It must have a copper roof, not lead as most do. Why is this cathedral not have a long arm to the cross? Remember in the video it was mentioned that sometimes towns ran out of money, or that the vaults would sometimes collapse? The cathedral in Monaco doesn't look right at all - it isn't Gothic, is it? No, it's Romanesque.
Let me emphasize here, both from parental pride but also it is important: he was asking the questions. He had taken the material on Gothic cathedrals and was now applying it to interpreting aerial photographs. I was just there to confirm his suspicions and make checks (in Wikipedia, of course!). Of course, some of the joy was in the spontaneity; turned into a regular assignment it might lose some of its charm. But this is, in my opinion, how to correctly approach the wealth of new resources. Instead of cramming onto a mental map of the old, treat them on their own terms. In a world where Wikipedia is almost always available and mostly right, prepare students to still think critically but also to leverage resources such as this. Otherwise, schools are simply wasting time preparing for a vanished world of yesteryear, rather than priming students for the amazing informational world that exists today.