An anniversary (from the Latin anniversarius, from the words for year and to turn, meaning (re)turning yearly; known in English since c. 1230)
Ok, so it does specify it's a yearly occurrence, I never realized, that I've always heard it used as "6 month anniversary" or "3 week anniversary".
I guess if you think of 1 year as the whole number measure of anniversary, you could have fractional versions of that time period. So "1 month anniversary" would mean "the 1/12th fractional part of the yearly re-occurrence of that date." which is how people tend to use it.
I'm a computer/math geek, I'm comfortable with using measurements in non-integer units :)
I do understand the frustration though, the root of the word translates into a very specific concept. The problem is the way people use words isn't very specific, which is why the language changes over time, words that once meant something take on different connotations.
Keep in mind, that at the root of all language is just a grunt sound that's assigned meaning. Structures of language are fairly arbitrarily built upon that basic core.
My favorite BTW is talking about people who verb nouns :)
Back when I was in the (sickeningly sweet) habit of celebrating those* I made a point of calling them "luniversaries." As a bonus, it lets the object of your affection know that you're still crazy about them.
* 192 months next week. I stopped counting a while ago.