If centripetal force is directed toward the center why do you feel like you are thrown away from a center as a car goes around a curve ?

Because you're trying to move in a straight line, and the force
on you is pulling you to stay on the circle.  If it happens to be,
say, the inside of the car door that's exerting that force on you,
to pull you onto the circle, then you feel a great force between
you and the door as the car goes around the curve with you in it. 
Door exerting a force on you, you trying to push out through the
door, what's the difference anyway ?  It's all the same to your brain.