Why do so many prefixes mean "Not"
Solution 1:
The negative prefixes usually have a rather complex developmental history, and there is usually some overlap into similarly negative meanings. The following nuances can thus be considered as general, rather than specific.
• a- atypical / an- anaerobic: These are the same - compare a cat/an egg. A-/an- = without/ outside of / absent(prep.) Compare amoral = outside the category of “moral”; that cannot be characterized as either morally good or bad. "Amoral" is basically neutral, (although when applied to human activity and because humans are expected to be moral) it is chiefly negative, and immoral -> contrary to “morals”: this is basically negative.
• anti- anticlimactic, anti-clockwise (for Britons): anti+ X = in opposition to X/as opposed to X
• counter- counter-intuitive, counter clockwise: in the opposite direction or sense, with a contrary effect, or in opposition, or response. From the adverb counter c1446 in T. Wright Political Poems & Songs (1859) II. 224 Now ye han founde parfite, love welle your game; For and ye renne countre thenne be ye to blame. (Now that you have perfection, love well the object of your pursuit; for, if [you do not] you will be running counter, and then you will be to blame.) - Compare with contrary
• de- des- di-, dif-, dir-, dis- disengage, disconnect – dis: to undo that which is already done or was the state/condition. ((i) disaster = dis + astra = against the stars -> ill-starred -> the undoing of [expected] fate. (ii) Differ - Latin: dif- prefix + ferre to bear, carry.)
• il-, im-, in-, ir-, ig-. These are all the same. = not. These are all related to “un-“
• mis- misunderstand – this is the same “mis”- as in mistake = mistakenly; in error - both with a nuance of "unintentionally".
• non- non-traditional = outside the category of (very similar to a-/an-)
• un- unhappy = not.