Why Objects still move under the effect of fictitious force? As I read in many books and websites, An inertial force is a force that resists a change in velocity of an object. It is equal to—and in the opposite direction of—an applied force.
If the inertial force (P) is equal to the applied force (F), then the net force (P+F) affecting the object is equal to 0. I wonder why object still move although the net force is 0.

 A: The inertial force P is a force perceived in the accelerating reference system. It does not add up to 0 in the (non-accelerating) resting reference system in which the force is applied to the object. Therefore, in the resting reference system, your body will be accelerated according to your force F and newton's 2nd law. 
A: By inertial force I suppose you mean: $F_{inertial}\equiv ma$. In problems involving accelerating bodies, people do apply $-F_{inertial}$ to the body, so that the problem reduces to one of static equilibrium (because net force on the body would then be zero), and so perhaps helps them think better. It is only a ruse. You may think of $-F_{inertial}$ as the force that needs to be applied externally by some means if you wanted the body to achieve static equilibrium. If you have not applied such a counterbalancing force then the body cannot be in equilibrium, but will accelerate.
A: Real forces are always interactions between two objects.   If we think that a force, such as your inertial force, is acting on an object, we should try to identify the other object.   If we can't, then we were wrong; there is no force.
The inertial force in your hypothetical problem does not pass that test.   You have imagined and applied force that does not exist.    There is no force opposing the applied force F, so there is no contradiction.
The inertial force which does exist in your scenario is applied by the block on whatever object is applying F to the block. That inertial force and F make up a third law pair.   But the behavior of an object is determined by the forces exerted on it, not by the forces it exerts.
