Compare with an umbrella uttered as /əmˈbrelə/, versus a university uttered as /juːnɪˈvɜːsɪtɪ/. Though both begin with the same written vowel, they have a different sound at the beginning. Umbrella has a schwa, while university has a 'you'. It is the sounds rather that the written vowel that drive the choice of 'a' or 'an'.

It is similar with your question. "An Eff Tee Ay" or "an Eff See". It is the spoken'Eff', uttered with a vowel sound as /ef/, that drives the use of 'an' even though [f] is listed as a consonant.