No, a table fan cannot lift an aeroplane. Even the most powerful household table fan generates only a small fraction of the airflow and thrust needed to lift a plane’s weight.
I have done some basic aerodynamics experiments and one thing that often surprises people is that “wind” alone does not guarantee lift. By moving the wings of the aircraft through a large volume of air, at a high enough velocity, and at the proper angle of attack, lift is generated. A table fan might produce a noticeable wind on your face, but the energy in that wind is tiny compared to what it takes to lift even the lightest airplane.
A typical table fan consumes around 40 to 80 watts of power. In contrast, the engine on a small training aircraft can produce over 100 horsepower, or around 75,000 watts. Large commercial aircraft use engines capable of producing tens of millions of watts of power at takeoff.
The real limitation is not only wind speed. It's volume of air, pressure differential, and total thrust.
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The air flow is focused on a very small space.
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The air velocity drops off rapidly as you move away from the fan.
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Fan blades are designed to cool people, not to produce high thrust.
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Aircraft wings need to maintain a high speed airflow over a large wing surface.
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A table fan can generate a lifting force many thousands of times less than the weight of the aircraft.
I have seen classroom demonstrations where a small foam wing is placed in front of big fans and they seem to "fly". This can lead to the misconception that any fan can lift an airplane. The important thing is that these models are only a few grams and are designed specifically for low speed aerodynamic testing.
One interesting exception always confuses people. If you made a very light model aeroplane weighing only a few grams then a strong enough fan could produce enough airflow to generate lift. This is often seen in wind tunnels where researchers test scaled models. But that doesn’t mean the fan is lifting a real airplane. The model is light enough that the aerodynamic forces are meaningful.
A useful analogy is to imagine trying to push a fully loaded truck with a hair dryer’s worth of air coming out of it. You can feel the air flow but the force is not enough to move something that heavy. The same is true of a table fan vs the huge aerodynamic forces required to lift an aircraft.
Also read: Aircraft and rockets is lighter than air according to its size?