Why did Gandalf leave Thorin and Company?

He did not abandon the Dwarves in Mirkwood. He had to help handle the problem of the Necromancer in the south part of Mirkwood. This was necessary because, when he had infiltrated the Necromancer's fortress, Dol Guldur, and found Thorin's father, he had found out that the Necromancer was indeed the Dark Lord Sauron, taking shape again.

Gandalf, along with the rest of the White Council, were afraid that Sauron would take notice of the great Dragon living just to the East of his fortress and form an alliance with Smaug, who was, perhaps, the last of the Dragons with the old fire. And so, while the Dwarves and Bilbo dealt with Smaug, Gandalf and others of the White Council attacked Dol Guldur, only to find that Sauron had fled (presumably back to Mordor, since that is where he is in LOTR).