Yes the use of A or An does matter because the words that you're going to use after those articles must either begin with vowels or sound like the word begins with a vowel.
Eg. An opinion, an elephant, etc...
A man, a comedian, a butterfly, etc...
But in this case the sentence is constructed to emphasis something using especially. Especially means to stress upon something (a word that is appropriately used in A, B and C). Specially means extraordinary or exceptional, it means special (a word that is not needed in this sentence).
C can be eliminated because "the capability of the respiratory system in dealing" is wordy.
B can be eliminated because "because of diminishing the respiratory system’s capability of dealing" changes the meaning of the sentence.
A is correct.