According to Newton’s Third Law of Motion, every action has an equal and opposite reaction. If one object exerts a force on the other object, the other object also exerts a force on this one. Hence if two objects, A and B interact, A exerts a force on B and B exerts an equal and opposite force on A. These forces act in two different bodies and they occur simultaneously, hence they do not cancel out each other.
For example,
In the diagram below, the swimmer pushes the water backward with a particular force and the water exerts a force on the swimmer with the same force. One force acts on water and the other on the swimmer, hence they do not cancel out each other.