Further to being offered a tracker rate of 3.67%, please find attached the latest letter from the bank
AIB's argument in that letter seems to turn on whether or not a tracker rate was "available" when your fixed rate period expired in 2013.
I would argue that trackers were in fact "available" in 2013 - thousands of AIB borrowers were on trackers at that time - they simply weren't offered to new borrowers or as a roll-off option for fixed rate borrowers. If AIB had meant that trackers had to be generally offered by AIB to new borrowers or as a roll-off rate when your fixed term expired for this option to be applicable, then AIB should have explicitly said so in their contract.
However, even if the word "available" should be read to mean "offered to new borrowers or as a roll-off rate", I think you could argue that by failing to offer a tracker rate as a roll-off option, AIB unilaterally changed an inherent and fundamental feature of the loan product, without your prior agreement.
I would definitely appeal AIB's decision to the FSO, with a copy to the Central Bank.
Hope that helps.