There is no good reason.
It's one of the Dumbest Lord of the Rings Moments.
The way it's presented in the movie it seems like one of the Fellowship could have helped him up. The Balrog's whip clearly was no longer attached to his ankle and the goblin arrows were landing well short of threatening anyone. My theory is that Gandalf pushed himself off because he knew that the Balrog had to be killed.
Doesn't explain why none of the other Fellowship (besides Frodo) tried to rush forward to help him. Even out of knee-jerk instinct. They all just stood there. If the archers were a threat they would take cover, but they literally stood there out in the open and watched Gandalf struggling to hold on.
I love nitpicking.