What seems to be most important about Poe's choice of a first-person narrator that is unreliable and a participant in "The Tell-Tale Heart" is his ability to convey the very thing the speaker denies is true: his insanity. Ironically, only the speaker is able to so clearly convey his failure to grasp reality, as the reader tries to follow his flawed and erratic reasoning.
The dramatic monologue begins with the unnamed (and highly unreliable) first-person narrator issuing a challenge of sorts...
The narrator wants to set the record straight, and the challenge must be in response to someone listening (in a jail or a mental institution) who has intimated that the speaker is crazy. Rather than insanity, the narrator tries to say he is simply nervous:
TRUE!—NERVOUS—VERY, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses—not destroyed—not dulled them.
In the introduction, the speaker acknowledges that he has a disease, but tries to explain that it is not a malady, but something with desirable results—that his senses are excellent rather than diminished. He speaks about his heightened sense of hearing:
I heard all things in the heaven and in the earth. I heard many things in hell.
This seems a clear indication that he has lost his mind, for who hears things in heaven and/or hell? It is his sense of acute hearing (its foundation found in his madness) that foreshadows the story's conclusion. With these kinds of details, the reader cannot help but arrive at a conclusion that the speaker is truly insane.
When searching his mind for motive, the speaker mentions all the positive things about the man that he is clearly aware of—things that seemingly might convince another to kill or not kill the man—but things that do not move him:
Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire.
He explains that all the rational motivations for murder (insult, greed, etc.) do not generate a desire within him to cause harm—in fact, he has no reason to do so. Neither does he have a passionate disposition that might drive him to an emotional and/or mental brink to bring on a break with reality or sanity. Instead, he notes that the old man's eye is the reason the narrator decides to plan the murder of the man who has been so kind and good. What a completely irrational statement.
I think it was his eye! yes, it was this!
Try as he or she might, the reader cannot follow this thread of reasoning because it is not based in rational thought, although he or she may try very hard to do so:
...the reader feels compelled to try to understand the method and meaning of the madness.
The dialogue that the speaker provides throughout the story allows the reader (while attempting to follow his skewed mental reasoning) to be convinced of the speaker's mental break. The details become horrific and the suspense rises as the speaker's panic becomes almost tangible. Rather than convincing the reader of his hold on reality, the reader is instead convinced of the speaker's seething madness. The imagined sound of the dead's man heart still beating is the narrator's undoing:
I felt that I must scream or die! and now—again!—hark! louder! louder! louder! louder!
“Villains!” I shrieked, “dissemble no more! I admit the deed!—tear up the planks! here, here!—It is the beating of his hideous heart!”
Had this story been told in the third-person, it would not have the same impact upon its audience. It is only in the mind of a crazy man such as this that while one attempts to follow the narrator's erratic thoughts, the reader can discover and be convinced that the criminal in the story has no reason or sound judgment. As he mentions early on, his obsession is only because of his hatred of the "Evil eye." Insanity is the only rationale for this statement, and hearing the narrator's thoughts is an effective way of allowing the reader to perceive the depth of his madness, and experience the horror of the speaker's actions—as Poe intends.