What is the origin of raison d'être?
The quasi-English phrase raison d’être “reason of being” is still unnaturalized, retaining a French pronunciation of sorts. The English noun reason comes from Middle English reason, raisoun, raison (with still more spelling variants), from Old French reason, reason, raison, etc., from Latin ratiō (inflectional stem ratiōn-), whose many meanings include “a count, calculation, reckoning (as in business or accounts), theory (as opposed to practice), faculty or exercise of reason.”
The French preposition de “of, for” becomes d’ before a vowel. De comes from the Latin preposition dē “away, away from, down, down from.” The development from dē to Romance de, di “of” can be seen over the centuries in graffiti, epitaphs, and personal letters. St. Augustine of Hippo defended vulgarisms (which after all became standard in Romance): “Better that grammarians condemn us than that the common people not understand.”
Être is the French infinitive “to be,” and as is typical in French, it is much worn down from its original. In Old French the infinitive was estre, a regular development of Vulgar Latin essere “to be,” from Latin esse. Esse in Latin is an archaism, and the infinitives of nearly all other verbs end in –ere or –āre, or –īre. In Vulgar Latin, however, esse is an anomaly, and the Vulgus “the common people” simple regularized esse to essere. (Essere is even today the infinitive of the verb “to be” in standard Italian.) French loses a vowel after a stressed syllable; thus essere becomes essre (esre), and esre develops an excrescent consonant t between s and r for ease of pronunciation. Raison d’être first appears in English in a letter written in 1864 by John Stuart Mill.