grammar - Why can we use "inadequate" but not "inspecific"?

I find the use of the word "inspecific" very natural. It makes sense and flows easily in sentences I speak and write (to myself at least). However, upon inspection, it is apparently not a valid English word, instead being nonspecific (A.H.D. 5), unspecific (O.D.O.) or something of that sort.

We use the in- prefix to negate the primary meanings of words very often, for instance in the words "inadequate" and "invariable". I feel like ignoring all of the signs telling me to use "non-specific" instead of "inspecific" and go with what I find right. What about you? Do you find the word "inspecific" right or wrong? Why can't we negate it, like we negate many other words, simply through prefixing an in-?

Also, as a rule of thumb, Latin words usually seem to take the in- prefix when negated, whereas Germanic words seem to take the un- suffix. Variable, adequate and specific have Latin origins according to The Online Etymology Dictionary. Why does specific, a Latin derived word, seem to be an exception?

Answer

On the Wiktionary definition of nonspecific, it notes:

Synonyms

unspecific (less common), inspecific (much less common)

The entry for inspecific does include quotations.

Google n-grams shows for nonspecific,unspecific,inspecific that the ratios between them is approximately 1000:100:1 respectively, i.e. for every 1000 uses of the word nonspecific, there is only 1 use of inspecific. This makes it almost unheard of by most people.

As an example, my browser's spellchecker says inspecific is misspelt. So you can use inspecific, but you need to expect that you will be continuously challenged about it. You can avoid being challenged every time by using nonspecific instead, as it is the most common of the three words.