Yes, you know where this is going.
There is a good article on this topic by National Geographic: 'Sharknado' Got One Thing Right: Aquatic Animals Sometimes Do Fall From the Sky
One of the first claims the article makes is this:
In real life, of course, sharks don’t fall from the sky. But fish, frogs, and alligators do—and scientists think the likely cause is a weather phenomenon called a “waterspout,” a term first coined in 1738 by traveler Thomas Shaw.
It supports this premise with historical anecdotes where people observed various animals falling from the sky due to waterspouts and tornadoes: fish, frogs, even small alligators:
On December 26, 1887 the New York Times reported that Doctor J.L. Smith of Silverton Township, Kentucky, saw something fall to the ground. And then it started crawling toward him.
The good doctor went hunting for more alligators. He found six more, "all quite lively and about 12 inches in length."
However, a NWS spokesman says it is unlikely that a waterspout would pick up a shark:
Don't expect any sharks to drop in. "While the tornado is spinning air along the surface of the water, it's not necessarily like a vacuum where it's sucking up sharks or sucking up marine animals out of the depths of the ocean," Vaccaro said. "So odds are the sharks wouldn't even be close enough to be entrained in the circulation of the water spout in any way, let alone would they be lifted because they weigh so much."
Note some of the weasel words: "unlikely," "odds are," etc. What I want to know is this: how strong must a tornado or waterspout be to pick up a shark?
Let us make some assumptions:
The shark is swimming as close to the surface as possible where it is still able to swim and breathe, so the storm should be able to exert some force on the shark and its surrounding water.
The physical characteristics are a juvenile great white shark: 2.5 m long and a mass of 500 kg. (many of the sharks in the "movie" were on the small side: let us ignore the ones big enough to swallow a human whole)
This tornado or waterspout is strong enough to lift an object of the given dimensions, even if such storm strength is off the chart.
How strong would the waterspout or tornado need to be?
How strong of a force would the storm need to exert to lift the shark?
What EF classification would the storm be: if the storm is so strong as to be unclassified, how fast would the winds need to be?
I suspect the answer will have to do with differing air pressures and the suction force (lift) these air pressures can exert (similar idea to an airplane wing), but I only took one semester of physics in college and am not familiar with the specific equations and principles that could explain this.