|Style over substance|
Unfortunately (for the pseudoscientists), the laws of physics do not in any way forbid bumblebee flight; there are no papers that deny bumblebee flight, and no scientist has done so in a lecture, except, perhaps, ironically. To put it simply, it is possible to "prove" that a bumblebee cannot fly if you perform an extremely crude calculation (like forgetting to take into account things like the rate of flapping, the rotation of the wing, or the action of vortices), but a full aerodynamic calculation (to say nothing of getting all empirical and watching a bumblebee fly) will show that the bumblebee's flight works perfectly fine.
The origin of the statement is lost in the mists of time, but one version says that it was made by French entomologist August Magnan in 1934, based on calculations by his assistant, an engineer. Other versions suggest that the bumblebee could not fly according to the principles of fixed-wing aerodynamics; that is to say, it must flap its wings. In fact, bumblebees simply flap harder than other insects, increasing the amplitude of their wing strokes to achieve more lift, and use a figure-of-eight wing motion to create low-pressure vortices to pull them up.
 The Kangaroo argument
There is a similar concept to the idea that a kangaroo can't exist because jumping would consume more energy than it could possibly get from eating. Like the bumblebee argument, it is possible to "prove" that a kangaroo can't jump if you leave out a few key variables. If you assume that a kangaroo is simply an 80kg weight that is lifted up and dropped repeatedly, then your calculation will show that the "kangaroo" can't jump. The missing variable is that a kangaroo's leg bones act as springs, transferring the energy from landing into the next jump.
 Mike Huckabee and the bumblebee
"It's scientifically impossible for the bumblebee to fly; but the bumblebee, being unaware of these scientific facts, flies anyway."