Why did Gandalf leave Thorin and Company?

Answer 1

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).

Answer 2

"The Thrushes are good and friendly-this is a very old bird indeed, and is maybe the last left of the ancient breed that used to live about here, tame to the hands of my father and grandfather. They were a long-lived and magical race, and this might even be one of those that were alive then, a couple of hundreds of years or more ago." Thorin also says that the men of Dale used to understand their language, and used them as messengers. Later, he proves faithful, and aids in the killing of the dragon.

Answer 3

He had his own business to attend to including meeting with the White Council and the attack on Sauron in Dol Guldur (in the south of Mirkwood Forest).

Answer 4

He and his fellow Wizards in the White Council had to deal with the Necromancer (who turned out to be Sauron).

Answer 5

gandalf left thorin and company at the boundaries of North Mirkwood, as they had just left Beorn's house (the man-bear person). NOTE: this is the west boundaries

Answer 6

Bilbo gives away the Arkenstone which puts Thorin in the position of having to parlay for it.

Answer 7

because bilbo gave the arkenstone to bard