I can't remember exactly now, but I'm sure there was some licensing dispute with Sony over Invincible. It was part of the ongoing public fallout with them but I think MJ wasn't allowed to preform any of the songs from the album live (at that time). I also read, he chose not to because at this time, he didn't want to even acknowledge the album's existence. Depends on what side you believe. Might have been in that Mike Smallcombe book, Making Michael I think.
As for why he chose Dangerous, he had a few go to songs (depending on the venue and occasion), Heal The World, Black Or White and Dangerous.
I think this was for a number of reasons but mainly he knew the songs inside out, he wrote them and he could lip sync to them. As for why Dangerous specifically, he worked on that choreography for so long it was a part of him, he could do it in his sleep. You can see the time and effort that went into that choreography, during the Dangerous Tour rehearsal tapes 1993 and during what we can see in the Travis Payne footage of the 1995 rehearsal. He loved that choreography and he was always trying to perfect it, which I've always found fascinating to see as I believe the 1995 MTV performance was a close to perfect as I've ever seen.
For me, I would have loved to have seen him perform Whatever Happens, that song is magical, in my opinion one of the best cuts off Invincible.
Although a lot like everything else on that album I feel it was missing more visual memories with Mike. Like when I hear Smooth Criminal, I think of the short film, the suit, the lean and so on. I don't have that feeling with almost all of Invincible, which is a real shame.
Great question by the way, it's always made me wonder too