There are many possible responses to this question. Montresor has lived with this secret for his entire life; indeed, after the murder, he indicates that "For the half of a century no mortal has disturbed" the bones of Fortunado, which means that no one discovered Montresor's evil murder of the man. So, imagine carrying around that secret for 50 years, knowing that you had murdered someone, but to tell it would mean that you would go to jail for murder. Because his confession would mean that he would go to jail for murder, I imagine one of several possible scenarios.
1. He is on his deathbed, dying, and knows that confessing the tale will hold no repercussions because he's just going to die anyway. Or, maybe he wants to get it out there so he can die with a "clean" conscience.
2. He has found a trusted confidant, that he feels he can tell this tale without them passing it on to the authorities.
3. He is burdened with guilt, and finally decides to unload the burden of his murder to a figure of authority, or someone who will listen and take the appropriate steps.
In my opinion, scenario #1 is most likely; if it is 50 years after the tale, Montresor has got to be very old. When the tale was told he was old enough to have a house with servants, so, at the youngest, in his 20's. Which would make him in his 70's when confessing the tale; it is very likely that he is on his deathbed. I hope that those thoughts helped a bit; good luck!