I've been considering asking this question here on Meta-English Language & Usage for the past few days pursuant to help-center guidelines and after just having asked several users about it, have been encouraged to do so.
So a question regarding the spelling (or more accurately the lack thereof) of inspecific was closed as a duplicate of another question was closed a long while ago. That question was Why can we use inadequate but not "inspecific"? However, the alleged duplicate, which is "Are there any patterns to observe in choosing the correct negation prefix to use?" does not seem to really be a duplicate in my opinion as it only asks for a generalized rule. If the rule of thumb given applied in this case, that would be fine and just, yet this is not the case.
The answer given in the generalized question is to the effect of "germanic derived words use un- and latin derived words use in-", but a trip to the Online Etymology Dictionary demonstrates that specific is ultimately, a latin derived word. The given answers do not make mention of specific exemptions, nor should they have to do so, because the question is only requesting a generalized rule. In a few words, the alleged duplicate is too "inspecific", so to speak.
The main reason for my concern is that with the redirection link as it is now, some of our less astute readers might receive the false impression that "specific" is germanic because it can use the un- prefix according to Collins English Dictionary — Complete and Unabridged 14th edition, and Google nGrams demonstrates that the although un- form, although overwhelmingly less popular than the non- form, has a longer tradition of usage. With things being as they are now, I suspect English Language & Usage could be a source of implicit misinformation, and I doubt any of us want that.
(Granted, it would be deceptive if I did not add that I have some degree of curiosity regarding the matter myself: The only reason I spotted this was because my first instinct was to spell the word as 'inspecific' and then wondered why my spelling checker highlighted it as wrong. I have reason to suspect that Star Trek is the bad influence upon me, but that is irrelevant to the subject at hand.)
Problematically, the question is also general reference as it is, since no research is demonstrated by the questioner, who is unlikely to return given three years of closure and presumably little other interaction with our website. However, I think that can easily be fixed without altering the core intention of the question by editing in a tagline like:
Exemplifying inadequate and saying "it sounded right" seems to suggest to me that the Latin etymology may have subconsciously influenced the questioner's instinct and curiosity, so I do not think this sort of edit would be too astray from the question as it was originally asked. Thank you for your consideration.