If the Karamazov brothers were a band, Dmitri would be the front man, the lead vocalist, the face of the group. The one who writes all the songs and gets all the girls. The one who could break out on his own and have a stunning solo career. But he'd also be the one to fall the hardest – the one who self-destructs on his own excesses, who ends up a washed-up has-been celebrity on one of those reality shows on E! or VH1.
Dmitri sweeps into Skotoprigonyevsk as a dashing military officer who breaks hearts left and right and spends way beyond his means. But this drunk, gambling womanizer has a taste for poetry, and we're talking really heavy, really dense German Romantic poetry, poetry that even native German speakers have a tough time understanding. He's a particular fan of Friedrich Schiller, who championed the arts as a way of wresting man from his brute, animal existence to higher thoughts and lofty ideals, like universal love and justice and peace (Read more about Schiller here.).
What's interesting about Dmitri's love for poetry is that he doesn't relate to it on an abstract, intellectual level. Let's face it: he'd probably fail miserably at Poetry 101. Instead, he seems to connect to poetry on an unconscious, emotional level. In the throes of passions that he can't describe or control, Dmitri often borrows bits and pieces of poetry in an effort to express himself.
It's the beauty of poetry that attracts Dmitri and draws him in: the way that it sounds and the images it conjures up. In fact, it might not be too extreme to suggest that Dmitri's connection to poetry is a sexual one. Just as he is seduced by the "infernal curves" (11.4.51) of Grushenka's body, it's poetry as a vehicle for beautiful images and sounds that sucks Dmitri in.
Just as his love for Grushenka propels him to seek out a kind of moral regeneration at the end of the novel, poetry also gets Dmitri back in touch with his basic, human desire for a higher order, for spiritual enlightenment – a desire that the novel suggests all men have (8.5.123). (Even Fyodor? Even Smerdyakov? We'll let you decide.)
Perhaps this desire for a higher order explains how a party-hardy military officer ends up with such elevated tastes. Even before he experiences a moral crisis with his false conviction for his father's murder, Dmitri reflects an awareness of how corrupt he is, frequently referring to himself as an "insect" (3.3.29) and "the lowest vermin" (9.9.5). It's hard to imagine how he could be so hard on himself without having some sense of what a human being could and ought to be.
Of course, not everyone grasps Dmitri's essentially good moral core. If you don't understand how fundamental a human's desire for higher order is, you probably look at Dmitri and see a rambling, selfish, amoral murderer, as the prosecutor Kirillovich does.
Tragically, Kirillovich's false view of Dmitri's nature wins out at Dmitri's trial, and Dmitri is sentenced to exile in Siberia for a murder he didn't commit. In a way, Dmitri seems to end up exactly where he was in the beginning of the novel. He's just as uncertain about what the right way to act is. Should he resign himself to his fate nobly and seek moral redemption through suffering? Should he escape to America with Grushenka? After everything he went through in the novel, you might agree with Alyosha that Dmitri doesn't have to prove that he isn't a vermin anymore.