Diet is a strange word. To most Americans, diet means short-term, weight-loss regime. To a more scientifically inclined audience, diet refers to the sum of food consumed by a person or other organism.
In a totally different context though, a diet is a political assembly. I first came across that use in ninth grade, if I remember correctly, when we learned that the Japanese legislature was known as a diet, following the German model. So, should it be pronounced deet?, I thought to myself.
No, it turns out, because it’s not a German word at all; it’s an Anglicized Latin word:
The term (also in the nutritional sense) is derived from Medieval Latin dieta, meaning both “parliamentary assembly” and “daily food allowance”, from earlier Latin diaeta transcribing Classical Greek diaita, meaning “way of living”, and hence also “diet”, “regular (daily) work”.
Through a false etymology, reflected in the spelling change replacing ae by e, the word came to be associated with Latin dies, “day”. The word came to be used in the sense of “an assembly” because of its use for the work of an assembly meeting on a daily basis, and hence for the assembly itself.
The association with dies is reflected in the German language use of Tagung (meeting) and -tag (not only meaning “day”, as in Montag — i.e. Monday — but also “parliament”, “council”, or other law-deliberating chamber, as in Bundestag or Reichstag).
The kicker is that the Japanese don’t use the term either:
The Japanese Parliament (the Kokkai) is conventionally called the Diet in English, indicating the heavy Prussian influence on the Meiji Constitution, Japan’s first modern written constitution.
So it’s a quasi-Latin term used by English speakers to translate a German term into not-quite-English — primarily when that German term isn’t actually used in Japanese.