One often comes across the following kind of statement concerning circular motion:

‘A particle moving uniformly along a circle experiences a force directed towards the centre (centripetal force) and an equal and opposite force directed away from the centre (centrifugal force). The two forces together keep the particle in equilibrium’.

Explain what is wrong with this statement.

For a person in the laboratory frame, this statement is wrong because w.r.t. observer in laboratory frame, the particle is in uniform circular motion which is  an accelerated motion. The acceleration of the particle is acting along the radius towards center. Therefore, force is required to revolve the particle in circle known as centripetal force and cannot be zero. 
But with respect to the observer in the frame rotating along with the particle, the particle appears to be at rest. Hence, the net force experienced by particle must be zero.
Therefore, the observer in this frame finds that some forces must act on the particle equal and opposite to centripetal force which keep the particle in equilibrium.
Therefore, the statement makes sense only with respect to the observer in the frame rotating along with particle i.e. non-inertial frame.