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what the misconception is here is that friction is the opposite but equal force being generated. when you puish on the floor so that you move the floor pushes back on you equally. seperatly from that as ypu moe over the floor the floor exerts a friction force on you and you exert an opposite but equal one on it. it is just coincidence that friction always apposes motion.
a general rule is that the force pairs are always of te same type. so if the earth exerts a gravitational force on me then i exert an equal gravitational force on the earth.
the way newton's second law is taught is often misleading if not plain wrong.
take the example of someone standing on the earth. you would probably have been shown that the earth exerts a force pulling you down therefore the earth has a normal reaction force in the opposite direction directly because of newtons second law. this is a simplification. what actually happens is the earth pulls on you so you pull on it. therfore the earth exerts a reaction force on you and you exert an equal reaction force on the earth. sometimes the simplification helps but i find when you start to think about tensions it just gets in the way.
coming back to the main point, the reason you slip is that the friction forces are less then the pushing forces. the opposing frictional forces and pushing forces are equal but opposite instead.
hope this helpd
Action-reaction law applies in the way that when u applied ur weight on the floor, u were stopped from entering the floor downwards by an equal and opposite reaction by the floor.U SLIPPED because of weak friction,and FRICTION ACTS PERPENDICULAR TO THE DIRECTION OF GRAVITY.So, although u slipped, the action-reaction pair between u and the floor was satisfied