Turns out, it's Kwik-so-tic, not Kee-oh-tic. It comes from Quixote, as in Don Quixote, the book, written in SPANISH. Seems like the pronunciation would follow the Spanish rules, but apparently, the Brits decided that "Kwicks-ote" (think oatmeal) was how to pronounce the man's name and it looks like they were the ones who coined the word quixotic. Cultural imperialism. Lame.
If you're wondering about other words you may have mispronounced (or correctly pronounced, if you asked me) check out this cool article about common English words disagreed upon regardless of dialect or linguistic background.