Why does the Speaker urging his wife to part from him quietly?
Similarly, you may ask, why should the parting couple melt and make no noise?
The speaker wants his lover not to mourn or cry (to "make no noise") for the loss of him because he does not perceive his death as a loss. Instead, he wants her to think of the two of them as being parts of a compass: one part stays standing erect in the center while the other part circles around it.
Similarly, it is asked, why is the speaker trying to console his wife?
Why is the speaker trying to console his wife in "A Valediction: Forbidding Mourning"? Throughout Donne's poem "A Valediction: Forbidding Mourning" the speaker attempts to comfort his beloved who is upset about their impending separation.
But to those who hear the bell tolling the news of this man's death, that affliction becomes a treasure because it forces us to feel pain on behalf of this other person, encouraging not only a sense of sympathy and connection with the rest of mankind, but also a contemplation of our own mortality.