"A soul hung up, as 'twere, in chains" (7)? Talk about a desperate housewife. This soul is hysterical over its confinement in the body. It's not just the creepy furniture—ropes of veins and arteries, too-loud ears; it's also the continual problems with maintenance. Whenever the body catches a disease, the soul has to endure the pain of both being sick and getting well again when all it really wants is O-U-T: "and ready oft the port to gain,/ Am shipwreck'd into health again" (29-30). One man's death is another soul's escape.
Whiny and self-centered, this soul is disgusted by the weakness and physicality of the body. Its rhetorical questions, posed to a possibly sympathetic who-knows-who, make it clear that the soul longs for higher and better things. It deals with real stuff, okay, like feelings and morals. It belongs in a more spiritual realm, not in this two-bit body.
The soul definitely doesn't have a monopoly on whining, but somehow the body comes off as more likable. It accuses the soul of acting maliciously—"And, wanting where its spite to try,/ Has made me live to let me die" (17-18)—keeping it alive and aware only to hit it upside the head with sin and death. Since when was that fair?
Plus, given that the soul gets to eventually re-join heaven, while the body has nothing but old age and a grave to look forward to, the body's complaints start to sound a little more legit. Although the soul sure doesn't see it that way, it looks like the dude with the skeleton got the raw end of the bargain.
That point is really driven home at the poem's end. It seems like Body and Soul have equal gripes, heading into stanza 4, but that Marvell chooses to end with the body, and give it an extra 4 lines on top, suggests that his sympathies lie more there than with ol' Mr. Soul.