TLDR
The pronunciation of 'iron' in standard varieties of English is EYE-URN (BrE: /'aɪən/, AmE: /'aɪrn/) and not EYE-RUN (which is also a common pronunciation of 'iron' in some varieties of English) because of a very common process called Metathesis. It's defined as the transposition/rearrangement of letters, syllables or phonemes (sounds) in a word.
Explanation
There are some other words that show the same change; 'wasp' used to be waps, 'bird' used to be brid and 'horse' used to be hros, but they've changed over time. Why is that?
It's because of a very common process called Metathesis. /'aɪən/ is the metathesised version of (/'aɪrən/). 'Iron' commonly used to be pronounced the way it's spelt (/'aɪrən/), but due to metathesis, its pronunciation became EYE-URN (/'aɪən/). Other words such as horse, bird, third etc., reflect the change in spelling; however, 'iron' doesn't reflect that change probably because metathesis applied to it after the spelling was standardised.
Metathesis:
Metathesis is defined as ’the transposition/rearrangement of letters, syllables or phonemes (sounds) in a word’.
Examples:
- 'wasp' used to be waps (wæps) [transposition of p and s]
- 'bird' used to be brid [transposition of i and r]
{Historical Metathesis}
'mix' being pronounced /mɪsk/ rather than /mɪks/ [transposition of k and s]
'desk' being pronounced /dɛks/ rather than /dɛsk/ [transposition of k and s]
'modern' being pronounced /'mɒdɹən/ instead of /ˈmɒd(ə)n/ (US: /ˈmɑː.dɚn/)
'pattern' being pronounced /pætɹən/ instead of /ˈpæt.ən/ (US: /ˈpæɾ.ɚn/)
Another famous example from Shakespeare's 'The Tempest' is the figure of Caliban whose name originates from a phonological metathesis of /n/ and /l/ in 'cannibal'. [ThoughtCo]
/r/-metathesis
Words having /r/ + vowel sequences are more susceptible to metathesis than others. According to A grammar of Old English Phonology by Richard Hogg, ‘R-metathesis normally occurs when /r/ is followed by a short vowel and a dental or alveolar consonant, usually /n/ or /s/’.
'Iron' is an example of /r/-metathesis. It was probably pronounced /'aɪrən/ (EYE-RUN) at one point, but it got metathesised to /'aɪərn/ (EYE-URN). However, the spelling remained unaffected.
Other examples of metathesis of /r/ include:
- bird from brid (bridde)
- third from thridde (ðridde)
- horse from hros
The silent R in 'iron' in BrE
The reason why the r in 'iron' is absent in British English is because the r is followed by a consonant (followed by /n/ in /'aɪərn/) and British English is non-rhotic, meaning the r is only pronounced when followed by a vowel. The same thing happened to 'bird', 'horse' and 'third' too (i.e. the r is followed by a consonant, so it's silent).
There are different types of metathesis, 'colonel' (pronounced KE(R)-NUHL /'kɜː(r)nl̩/) can also be said to be a product of metathesis. (See this answer on ELU for the spelling and pronunciation of 'colonel')
According to Wikipedia, the reason for ‘common speech errors’ is also metathesis.
Examples include:
- perscription for prescription
- interduce for introduce
- revelant for relevant
- foilage and foliage
References: