The structure is a hint as well, the punctuation is irrelevant in that sense.
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You are a:
While the text may be a disguised description of your functionality, the real clue here is that:
the number of letters in each word are 3-1-12-3-21-12-1-20-15-18, which when converted to letters via A1Z26 spells out CALCULATOR!
To attempt to decode the apparent mysticism of the text...
tap a cabalistical sum
'Cabalistical' implies 'secretive or mysterious'. These words describe the act of pressing buttons to find the answer to an unknown ('mysterious') sum.
counterdemonstrations, fabrications, I antienthusiastically circumstantiate unexceptionability
These words suggest that a calculator simply (with nothing extraneous merely for show, i.e. 'antienthusiastically') always generates the correct answers without exception. The use of 'counterdemonstrations' and 'fabrications' may be obfuscated ways of referring to 'subtraction' and 'multiplication', respectively - since, after all, a calculator performs calculations other than merely addition...
PS The OP explained their true intentions of the meaning of the phrase in comments below:
It really boils down to, "You can't fool a calculator." You can type whatever twisted stream of digits and symbols you can think up - cabalistical sums, counterdemonstrations, fabrications - but still it will perform its pre-programmed operations systematically, unemotionally, and without deviating from its rules (i.e. it will antienthusiastically circumstantiate unexceptionability).