This actually grinds my gears on two levels. First, of course, is the mispronunciation itself. The word is not pronounced like the unit of European currency; the correct Greek pronunciation is to ignore the leading 'G' and pronounce the 'Y' as 'yee' - so if there even was such a word it would be pronounced YEE-ro.
The second thing is that, at least as it applies to a food item made from a folded pita stuffed with sliced lamb and other fillings, there is no such word as 'gyro'. The word for a single one of these "Greek tacos" is actually 'gyros'. Despite ending with an 'S' the word is singular and would thus be correctly pronounced as YEE-ros; the plural (being a Greek word) would be 'gyri', pronounced YEE-ree.
And there you have my Daily Didactic Diatribe for Sunday, April 23rd.
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Now, cue the respondents who will claim that languages are constantly evolving; that "gyros" is just a loan-word anyway; and that American English usage of a foreign word does not mean that American English speakers are in any way, shape, or form obligated to pronounce the word correctly —
in five.....
four....
three....

-"BB"-