The coat of arms and the motto Montresor describes are suspiciously appropriate. It is possible that Montresor is inventing both of them as a cruel joke. He says a few lines later, "My own fancy grew warm with the Medoc." Montreor has been behaving in a zany fashion since getting his victim down underground. He does not have to be cautious any longer. He has a rapier and Fortunato, in his tight-fitting costume, must be unarmed. Montresor can kill Fortunato any time he wants to. Furthermore, Montresor is getting a little bit drunk. The Medoc may be the first wine he has drunk all eveninig. There is no reason to believe that anything he tells his victim is the truth. He has been lying to him since they met in the street. He lies about being a Mason. And, of course, the biggest lie he has told is that he has a cask of Amontillado in the catacombs beneath his palazzo.
It is possible that Montresor does not have a coat of arms at all. His background is suspect. Here he is a Frenchman living in Italy. Why? Although the catacombs are full of human bones, they are probably not the bones of Montresor's ancestors. The chains attached to the rock wall in the niche indicate that these catacombs and their contents go back a long time. Other poor wretches were chained there hundreds of years ago. Some of the bones piled in front of the niche may be the bones of people who died in those chains. Montresor may be hypersensitive about his family honor because his family history is so obscure. And Fortunato may know, or at least sense, that Montresor comes from an inferior background. Some of the "thousand injuries" Montresor has suffered may have come from insolent questions and remarks about his origins.
In short, Montresor may be making up a coat of arms and family motto because he doesn't have a genuine one, and Fortunato may be asking him about them just because he either knows or suspects that this is the case. As long as Montresor is inventing a coat of arms and a family motto, he might as well make up one that satisfies his outraged feeliings. If Montresor had told this lie on a different occasion (assuming it is a lie), then Fortunato might have checked it out; but Fortunato won't be checking anything out.
Though Montresor's family is not as illustrious as the powerful Fortunatos, he is proud of his heritage, and he obviously lives by the motto of his family coat-of-arms. When Fortunato admits to forgetting the image of the Montresor family crest, Montresor explains that its image consists of
"A huge human foot d'or, in a field azure; the foot crushes a serpent rampant whose fangs are imbedded in the heel."
(A large golden--"d'or"--foot in a blue field, it crushes an out-of-control snake who has bitten the heel of the foot.) The motto on the crest:
"Nemo me impune lacessit."
(The English translation of the Latin phrase is "No one attacks me with impunity.") One of Montresor's main points considering Fortunato's murder is that he
... must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser.
Montresor has decided to seek revenge on Fortunato by honoring the credo of his family crest--to kill without being caught.