What is Dante's sin?

We're not told, and of course he's not sentenced to hell for eternity, he's merely being taken on a tour of it.

At the beginning of the Inferno, he says that he had "lost his way". That presumably refers to something he'd done of which he was ashamed. He was married, so possibly it was a sexual sin, though he could also have been experiencing doubts about God or strongly negative emotions connected with his political exile and legal situation. The Comedy was born of this experience, as he imagines being put back on the right path by visiting Hell and then Purgatory and Paradise.

In Dante's 5th circle (Wrath) he and Virgil cross the river Styx in his skiff. On the way they are accosted by Filippo Argenti, a Black Guelph from a prominent family. When Dante was forced to leave Florence, Argenti took all his property. When Dante responds "In weeping and in grieving, accursed spirit, may you long remain," Virgil blesses him with words used to describe Christ himself (Luke 11:27). Literally, this reflects the fact that souls in Hell are eternally fixed in the state they have chosen, but allegorically, it reflects Dante's beginning awareness of his own sin. Just as Argenti seized Dante's property, he himself is "seized" by all the other wrathful souls. (Canto VIII).

This is taken from the Wiki link below. There may be more on Dante's personal sin but I just mention this point.

http://www.sparknotes.com/poetry/inferno/summary.html

I don't see that he sinned... he is led through hell, as he enters... there is an inscription ... he is taken through hell... and Beatrice is in heaven apparently and sent Virgil to guide Dante through hell.

Virgil leads Dante through the gates of Hell, marked by the haunting inscription “abandon all hope, you who enter here” (III.7). ((Dante is not fearful or hopeless... he trusts Virgil to take him through > signifying that he is not afraid of being imprisoned there)).


Virgil says that their path will take them through Hell and that they will eventually reach Heaven, where Dante’s beloved Beatrice awaits. He adds that it was Beatrice, along with two other holy women, who, seeing Dante lost in the wood, sent Virgil to guide him. Eventually, the poets reach the Lethe, the river of forgetfulness, and travel from there out of Hell and back onto Earth. They emerge from Hell on Easter morning, just before sunrise.

His sin was for loving Beatrice.

He was a bad dancer. Absolutely unforgiveable.

No

Inferno is only one part of Dante's Divine Comedy. He also describes Purgatory and Heaven. He was visiting those places in his work of fiction not assigned to any of them. Try reading it.

At least one of his sins was pride. That comes from his tour of Purgatory. Souls guilty of Pride were carrying heavy things because they had elevated themselves too much in life and they were pressing themselves down. Dante started carrying the heavy items because he recognized pride to be one if his sins.

This is just from memory so you should check it.