In "The Cask Of Amontillado," why was it effective to explain about whether or not the narrator was part of the "brotherhood" of the Freemasons?

In the story, it seems that Fortunato makes reference to the Freemasons as just one more way of belittling Montresor, even more than the "thousand injuries" he's already inflicted have.  As Montresor leads the wine connoisseur deeper and deeper into the crypts toward the nonexistent pipe of Amontillado, he stops to offer Fortunato wine so that by the time Fortunato realizes Montresor's intention to wall him in, he will be in no shape to fight.

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In the story, it seems that Fortunato makes reference to the Freemasons as just one more way of belittling Montresor, even more than the "thousand injuries" he's already inflicted have.  As Montresor leads the wine connoisseur deeper and deeper into the crypts toward the nonexistent pipe of Amontillado, he stops to offer Fortunato wine so that by the time Fortunato realizes Montresor's intention to wall him in, he will be in no shape to fight.

On one of these wine stops, Fortunato "laughed and threw the bottle upward with a gesticulation [Montresor] did not understand."  When Montresor looked at Fortunato in surprise, Fortunato repeated the action.  When Montresor failed to comprehend, Fortunato responds triumphantly, "'Then you are not of the brotherhood [....].  You are not of the masons.'"  Once again, Fortunato attempts to exclude Montresor, to point out that he is somehow less than Fortunato because he doesn't belong to this organization which is veiled in secrecy and steeped in tradition and symbolism.  Montresor cries, "'Yes, yes, [...] yes, yes," and to prove his membership, he produces a trowel from beneath his cloak.  Fortunato has clearly given the secret sign of membership to the Freemasons, and in an effort not to be again bested by him, Montresor claims that he is a member (which he is not, or else he would have recognized the gesture).  However, what Fortunato does not realize (either because he is too proud or too drunk, or both) is that it is quite odd for Montresor to be concealing a trowel -- a tool used to apply and spread mortar -- on his person.  This is precisely the tool a person about to build a wall, like a mason, would carry.  Although the fact that Montresor carries a trowel with him doesn't seem to make much impression on Fortunato, readers who are blinded neither by pride nor drunkenness, ought to question its presence.  In total, the interaction offers us some significant foreshadowing as we might begin to guess what Montresor's response will be to those "thousand" and one injuries he's endured.