Montresor was very specific in the beginning to explain that Fortunato had "wronged him" and deserved punishment. However, in order for that punishment to be fair and just to the insults hurled upon Montresor, it had to be done secretly This secret, as Montresor says, is "not only punish, but punish with impunity''; that is, to punish Fortunato without being caught or punished himself. Therefore, he can not confess to the crime. We can assume that this confession is being done towards the very end of his life, perhaps even on his deathbed, when not punishment could be exacted upon him.
In addition, Montresor is an unreliable narrator. He is obsessed with injuries that he does not even describe in detail, suggesting perhaps that those injuries were not as damaging as his violent act suggests. The lack of remorse he shows 50 years later, coupled with the passioned explanation of his actions that he makes, help to support the idea that this is an unstable man run amuck with perceived insults, and not a sane man dealing out deserved punishment.