Actually it’s not even that simple.
If it were merely initialism it would be: G-I-F sounding it out to GEE EYE EFF ( 3 syllables) ; but 'JIF" sounds out to “JEEEF” ( 1 syllable) sounds too forced too different from “GEE EYE EFF”.
The hard G version sounds more natural ( at least in English ) “Gift” w/o the “t”.
Maybe it’s just tech curse of web tech. to always have two arguing versions.
Whenever I hear ‘Jif’ I think of their better know competitor ‘Ajax’.
Ha ha, although I’m not sure Jif the cleaning agent is known about outside Australia, unlike Ajax.
All I can say now about the pronunciation ‘jif’ for .gif is GEE EYE EFFing hate it. 
It was called Jif but got renamed to Cif a few years ago. I think it’s called Cif throughout Europe
:eek2: I suppose that means there will now be an argument over whether it is pronounced “Kif” or “Sif”. 