How come many Americans say Eye-rack, instead of Iraq... but no one pronounces Italy as Eye-taly?
Phonetically, it is called 'free variation'; observe the same phenomenon with 'either'.
However, I suspect the reason for this is more likely the following: 'Italy' has historically been in the English lexis for many, many centuries whereas Iraq has not; there is a natural tendency in every language to construe vowels in such a way as to be convenient to the respective speaker. Observe the phenomenon in the UK: 'garage'; this represents a shift towards a more English pronunciation of things (stress on the first syllable as opposed to American pronunciation). We tend to pronounce the vowel 'I' as a diphthong in English and I think the case of Iraq is one of phonological levelling, in which the foreign sound in assimilated into the familiar sound.