How is "To His Coy Mistress" a three-part argument?

To answer this question you need to think about the
structure of the poem that Marvell creates and consider how the poem is actually divided
into three discrete sections, and how each of those sections are used to advance the
speaker's argument.

The first section runs from lines 1-20,
and consists of lots of examples of hyperbole as the speaker tries to describe the
extreme lengths to which he would go to express his love for his beloved if he had but
time to do so:

My vegetable love should
grow

Vaster than empires and more
slow...

However, in lines 21-32, the brevity of life is
stressed as the speaker reminds his beloved that they do not have eternity to court. In
reality, time is described as a "winged chariot hurrying near." The only future they
have to look forward to are "deserts of vast eternity." Based on this, lines 33-46 move
to the conclusion of the poem, as, with a tone of challenge and defiance, the speaker
urges his mistress to "devour" time and "tear" the pleasures from life, because time
cannot be made to stop. By so doing, the speaker argues, they can make the sun
"run":

Let us
roll all our strength and all

Our sweetness up into one
ball,

And tear our pleasures with rough
strife

Through the iron gates of
life;

Thus, though we cannot make our
sun

Stand still, yet we will make him
run.

Thus each of the three
sections of this poem is clearly built on upon the other and helps to advance the
central argument of why it is important to love today and not wait for a tomorrow that
may never come. "Coyness" is thus a "crime" based on the brevity of time and our
inescapable death.