You're right. No need to convince me.
It's not a real force, but an apparent force. For circular motion, one needs a force to pull the particle/object towards the center. Inertia wants the object to keep going straight. So there is an apparent force on the object to resist the inward force. What it really comes down to is that Angular Momentum is conserved, therefore the object experiences a resistance to being pulled in.
Mathematically, the "centrifugal force" term comes from the "ma" side of F=ma (from Young and Freedman, University Phyiscs). So it's not a Force. Since it has the units of force, it is often taught to freshman physics students as a force (but good text books don't). This is an example of how just because something has the same units as something else doesn't mean they're the same thing. I guess a good term would be "pseudo-force."
Now I have to address something another responder said:
The center of gravity is just an "imaginary point" but a point of physical significance. It's the center of mass. Now if you were in the center of a hollow Earth, it's false to say that you would be pulled outward in every direction. In actuality, one can Mathematically show that gravity would be completely canceled out in a hollow spherical Earth. You wouldn't feel any gravitational atttraction at all. You don't even have to be at the center, but could go to the very edge. There would be no gravity. This is due to Gauss's Law. Weird, I know, but very true.