It's not taboo. The "why" is redundant - we don't need it. The reason... The reason why... Both phrases have the same meaning. But as you've observed, "the reason why" is commonly used. I wouldn't judge the phrase as incorrect or bad English.

I've never heard that it was "taboo" and I don't believe it. It sounds like a usage myth to me. Usage and grammar aren't perfectly logical, and just because something is redundant doesn't mean that it's incorrect. Usually, it is good style to cut out unnecessary words. My first reality check is to do a Google search of the writings of George Orwell at Project Gutenberg Australia. The reason why I choose this as my first test is that I consider Orwell to be a superb prose stylist, and a person very concerned with economy in writing style. I find: "The reason why class-hatred seems to be diminishing is that nowadays it tends not to get into print..."--The Road to Wigan Pier "There is really no reason why a human being should do more than eat, drink, sleep, breathe, and procreate; _everything_ else could be done for him by machinery."--The Road to Wigan Pier "But in truth the reason why Mrs Creevy had sacked her was quite simple and adequate..."--A Clergyman's Daughter "But the real reason why I should not like to be in the book trade for life is that while I was in it I lost my love of books."--essay, "Bookshop Memories" "The reason why such a suggestion sounds hopeless at first hearing is that few people are able to imagine the radio being used for the dissemination of anything except tripe."--essay, "Mark Twain, the Licensed Jester" ...and on and and on. There are literally dozens of uses in Project Gutenberg Australia's collection of fifty Orwell essays, and that to me settles it. Searching the regular Project Gutenberg corpus, I find uses of "the reason why" by David Hume (the philosopher), by H. L. Mencken (author of "The American Language" and very particular about usage), by Lord Byron (in the poem "Don Juan," where he uses it for a rhyme so perhaps that shouldn't count), Oliver Goldsmith, Herman Melville, Mark Twain... There's no reason why it should be considered taboo.

SUMMARY: 1) The three-word phrase "the reason why" is not taboo. There is nothing wrong with it. Famous classic English and American writers use it. 2) There are some contexts, such as the end of a sentence, where the "why" is redundant. It's not wrong, but it is better style to omit it. An example would be "I can give you several reasons."

There might be certain instances in which "the reason" is clearly better than "the reason why," although even here I don't see it as wrong: "If you're going to drop Mentos in a bottle of Diet Pepsi, don't do it here in the kitchen, go outside." "OK, but I want to know the reason [why]." The more I think about it, the more I think that if you have to make a flat rule, in most of the examples, including the ones I quote above, it makes me slightly more uncomfortable to leave out the word "why." To pick another example--this time from William James, "Pragmatism" (I Googled, I'm not that well-read) "The reasons why we call things true is the reason why they _are_ true..." (Twice in one sentence!) If I rewrite this as "The reasons we call things true is the reason they _are_ true..." it does _not_ feel quite right to me. It feels to me that the word "why" ought to be there, and is understood to be there even though it is missing.

Thanks Paul.