The burning legion doesn't have a home, i think you're confusing them with the original horde (y'know, just the orcs).

...because Outland ISN'T the homeworld of the Burning Legion. The Legion comes from a multitude of planets throughout the Twisting Nether, but Draenor is not one of them. In fact, between the end of Warcraft II and Illidan's entrance into Outland, the place (what was left of it) was relatively peaceful, if you consider the insane wildlife, occasional attempts at invasion, and recovery from being shattered "peaceful."
Illidan's entrance into what is now called Outland attracted the Legion's attention, and they decided to try and use Illidan to gain greater access to Outland, and from there invade Azeroth. At the end of Warcraft III, he turned on the Legion, which is why he's making his armies right now. So the Legion has, at best, a foothold.
It also means that Kazzak really broke open the portal FAR too soon, not realizing that those puny humans he had a habit of chowing on were stronger than the majority of his soldiers. Good move, Kazzak, we kicked your army's ass, and are doing a damn fine job of keeping them at bay while we clean up the Legion's messes for you!

Actually the Burning Legion had known about Draenor for a pretty long time before Illidan got there and decided to take over. Think before the original Warcraft.

And the Outlands we know today was once a continent on Draenor, with ocean all around it. There's a dock and a ship sitting off the edge of Netherstorm, for example. Hellfire Peninsula used to be a REAL peninsula.

My point was that, after the Horde was defeated, the Legion lost interest in Draenor for the most part. Seem to have skipped that part somehow. And the fact remains, Draenor is another place the Legion failed to properly invade, and has continued to fail to invade properly, though largely because it's not as interesting as Azeroth.

Outland was never the Burning Legions homeland to start with. Read the novel Rise of the Horde for more info on that.