reference frames - Why is centrifugal force considered fictitious ...

Why is centrifugal force considered fictitious, when it's the one that feels real to us when we are moving in a circle? I understand the explanation regarding the reference frames: if our body is the reference frame, and it is rotating, a fictitious centrifugal force needs to be made up to cancel the centripetal force and explain why we appear to be stationary in relation to ourselves. However, if we are in a round up ride, we feel pushed againsts the wall, rather than towards the center of the ride, which would be the centripetal force. So if centrifugal force is the fictitious one, wouldn't that be like saying that the force we feel pushing us againsts the wall is only in our minds?
$\begingroup$You may not have given enough thought to what "we feel pushed" means. If you think through some more day-to-day instances you'll find that there are two different ways to interpret that phrase. One that is consistent with the way we talk about gravity and one consistent with the way we talk about everything else. There is a reason for this. How does it feel if a friend pushes you unexpectedly from behind; how does your body move and how do your loose limbs move. What happens if a sliding sidewalk stops unexpectedly (noting that it is only in contact with your feet).$\endgroup$
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Suppose you're in a fast car and you stomp on the accelerator. You feel pressed into the back of the seat. In which direction are you accelerating? Forward, obviously, but you feel a force pushing against your back. Now you turn a corner. Your seatbelt, and maybe the door next to you, press against your side. In which direction are you accelerating? In this case, it's not so obvious, but it's inward, not outward. There is no centrifugal force here.
In both cases, the side on which you feel the force is opposite the direction in which you are accelerating.
$\begingroup$So which force makes us feel pushed againsts the wall in a round up ride? From your answer I understand it is not the centrifugal force. Is that a third law partner to the centripetal force? I'm a little confused about how to name the force acting on our body outward from the the center of rotation, which feels like a real force.$\endgroup$
$\begingroup$@Auggie -- There is no outward force acting on you. The forces acting on you are gravitation, which pulls you downward, friction against the wall, which opposes gravity, and the normal force by the wall, which pushes you toward the center of the ride.$\endgroup$
$\begingroup$So, just to clarify, when you say there is no outward force acting on us, you mean in an inertial reference frame, right? what about in a rotating reference frame? And then, going back to my original question, is the force that we feel in the outward direction only an illusion? I'm a beginner and an amature, so I appreciate your patience :)$\endgroup$
$\begingroup$@Auggie - What you feel in that ride is very similar to what you feel in an accelerating car when the back seat of the car pushes on you. I hope you agree that there's no force pushing you into the seat. It's the same for the ride. That push by the wall of the ride (or by the back of the car seat) against you propagates through your body. Your body is a mix of bones, cartilage, and soft tissues that respond differently to that push. You feel that push internally as well as externally.$\endgroup$
The reason we feel that we are pushed outwards is due to inertia. Inertia is the resistance to movement. It is measured by mass. When we have more movement, it makes it harder to get us moving.
In a car that is on a curve, for example, our inertia makes us want to keep on going forward. Going forward in this case would make us feel that we are being pushed outwards. Therefore, there is no centrifugal force in this case.
Sometimes, the centrifugal force is referred to the reaction force of the centripetal force. But usually, it refers to a ficitious force used to simplify thr mathematics.
$\begingroup$The idea of centrifugal force is not used to simplify the mathematics. Just the opposite. Centrifugal force exists only in the rotating frame of reference, and it complicates things. Much simpler to analyze the situation from a non-rotating frame of reference, where it becomes obvious that a body can not revolve around the center unless a real force continually pushes it toward the center.$\endgroup$
We say fictitious because the actual source of the centrifugal acceleration is somewhat indirect and the experience one has results from the unbalanced forces acting on the reference frame, not a force. Note, it is an acceleration not a force.
For instance, imagine yourself on a swing. The swing seat is constrained to move in a circular arc by two opposing forces, gravity and tension. Those are the only two forces acting on the seat, yet while swinging, the seat is not in an inertial reference frame. So if you sit in the seat and constrain yourself to the seat (i.e., you don't fall off), you will be accelerated just like the seat because the tension and gravitational forces do not balance. The only place in the arc where you do not accelerate is same place where the seat would rest in equilibrium (i.e., just hanging there if left alone). Note that there is no centripetal or centrifugal force here, just tension and gravity. These two terms only apply to discussions of the acceleration of the reference frame or object. They are not forces and should not be called forces.
The point is that centrifugal acceleration only exists in non-inertial reference frames, namely frames of reference that are accelerating. It is not a force, only a term in the acceleration vector resulting from the frame of reference in which you calculate the acceleration. There is a useful animation found on the Coriolis effect Wikipedia page.