The short answer is because our English spelling system is not rational. It is not based on rules. How we spell is oftentimes a mixture of etymological wishful thinking and historical accidents.

For the long answer we have to look at the languages that present-day English are decended from: Middle English and Old English. Fire in Old English (sometimes called Anglo-Saxon) was fȳr (alt. fīr). By the time Old English had turned into Middle English, fȳr had become fīr (also spelled fier, vir, fer, ver, feir, veir, fur, fuir, vur, feur, feor, foir). What happened? Why so many different spellings. Well, some big changes took place between when Old English and Middle English were spoken and written. Old English was pretty much written as it was spoken (and there were a few dialects), but towards the end of the Old English period, one dialect and its orthography were used in the chanceries of all the different English kingdoms. The in 1066 CE, a Frenchified Viking named Guillaume conquored those Old English kingdoms and became William the Conqueror. Old English was replaced by the Norman dialect of Old French. By the time English again became the language of the English court, Old English was long gone, and Middle English took its place. Many of the literate people (monks usually) had been trained in the Norman spelling system, and when they started to write down Middle English they used a mixture of the old Old English orthographies and the new-fangled Continental systems. Then another huge linguistic event took place: the Great English Vowel Movement. Most of the vowel sounds in English changed how they were pronounced. That's why English "long" vowels (actually usually diphthongs in the Early Modern to Present Day English are not pronounced like the rest of the Europeans languages pronounce them. (Think Italian vowels or Spanish, instead of the English.) Fiery was first recorded in the Middle English period written something like furie. By the time of Nathan Bailey's dictionary (1721) and Dr Johnson's (1755), the spelling had been fixed as fiery.

Ceci n'est pas un seing.