The poem is built around a simple and persuasive structure, that I think of as "If - But - So."

The logic is simple and straightforward.  "If we had world enough and time . . ."  the opening section evokes what would happen in an ideal world.  The "coyness," or reluctance of the lover would be no crime, because there would be no urgency.  They could each take their own sweet time, and go about their business on the opposite sides of the world if necessary; if only they "had world enough and time."  Be wary of the lyricism of the opening argument.  It is designed to put you off your guard.

But, the narrator tells us, "time´s winged chariot draweth near," they are subject to a limited amount of time, just like the rest of us, and reminded here of their own mortality.  The mid-section is full of references, often grisly and macabre, to the tomb and their own impending deaths.  Clearly the lover, speaking to his mistress has a pretty firm agenda in drawing her attention to her impending death.  He is determined to seduce her.  The poem is thus a resonant anthem for a kind of Carpe Diem attitude that we see elsewhere phrased a little more politely (see, for example, Rober Herrick´s wonderful "To the Virgins, make much of time").  But perhaps a modern audience rightly shrinks from a brutal logic that says, `keep your virginity if you like, but if I don´t take it, those maggots will!´  The persuasion perhaps tips over into aggression in the latter stages of the ugly mid-section which leaves us perhaps less than enthused by the closing argument.

If we had time, we could wait, but we don´t, so . . .

Now let us sport us while we may,
And now like amorous birds of prey,
Rather at once our time devour
Than languish in his slow-chapped power.

We may well have a great deal of sympathy for the attractive, if slightly visceral, simile describing the lovers cavorting like "amorous birds of prey," and devouring time, rather than let it devour them, but perhaps the final impression that the poem leaves is of someone being persuaded against their will, to do something that they would rather not.  Is the Coy Mistress a playful participant in this process, or a guileless victim of an unprincipled rogue?  Does Marvell wish us to cheer for the hedonistic common sense that tells us, as Herrick tells us:

Gather ye rosebuds while ye may,
Old time is still a-flying,
And this same flower that smiles today,
To-morrow will be dying.

The choice, I think, is yours.  I´m curious to see what you think.