Well, since it is the biggest, it can't be either Alaska or Southwest, that's for sure.
It depends on how they mean big:
American Airlines has more planes than any other in the world, totaling in excess of 700.
Delta flies more passengers than any other line in the US.
United has more flights/routes than any other in the US.
So I am predicting United. And no, I don't think they are anymore dangerous than AA, DL, CO, TW, or anybody else, for that matter.
Just my two cents.