We don't know, although the best explanation probably is, "Dante didn't want to."

Dante wrote a number of poems and sonnets in his local vulgate, as well as an unfinished (ironically in latin) work titled De Vulgari Eloquentia, where he had set out to examine and defend the use of the vulgates all over the world, including his own. Dante is also framed within the wider trend of writers in Tuscany abandoning latin in favor of the the local vulgate: Giovanni Boccaccio and Francesco Petrarca are two other notable examples.

That being said, the use of the vulgate in the place of latin was a long debate in Italian intellectual circles, which preceded the debate about the best variety of Italian to use. I actually wrote about this a week ago, here.