Why is centrifugal force ‘fictitious’?

Centrifugal forces only arise when you treat a non-inertial frame of reference as if it were an inertial frame of reference. Consider what happens if I accelerate past a stationary object and I consider the motion of the object in a frame of reference in which I am at rest. I observe the object accelerate in the other direction. Since the mass of the object is constant, and Newton’s 2nd law gives F = ma, the fact that the object accelerates leads me to conclude that there must some force accelerating it. The same happens if I am in a bus which is accelerating (either by changing speed in the same direction or by changing direction). I witness the stuff, including me, accelerating around the bus but only because I am considering the bus and its contents as at rest in an inertial frame of reference.

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