The infamous case of the flightless bumblebee is a classic example of being careless with approximations.
It stems from someone trying to apply a basic equation from aeronautics to the flight of the bee.
The equation relates the thrust required for an object to fly to its mass and the surface area of its wings.
In the case of the bee, this gives an extremely high value, a rate of work impossible for such a small animal. So the equation apparently proves bees cannot fly.
However, the equation assumes stationary rather than flapping wings, making its use in this case misleading.
Of course if equations fail in physics there is always empirical observation, if a bee looks as if it is flying, it most probably is.