If centrifugal force isn't real then why am I being pushed on a merry go rournd? I just finished my class on circular acceleration and I learnt that centrifugal force (outward force) is a psuedo force. It doesn't really exist. 
Now suppose I am going round in my car or a merry go round or whatever. I feel like a force is pushing me from the center and towards the window of my car which is in the opposite direction from center. Now how this be explained? 
I asked this to my teacher but he gave an explanation with inertial reference frame which I didn't really understand. 
Pardon my grammatical and spelling mistakes.  
 A: Centrifugal force is a pseudo force like this is a pseudo killer whale.

Just because it's "pseudo" or "fictitious" doesn't mean it's not real. It's just as legitimate a whale whether it's called "pseudo killer whale" or "grey pickle whale". Through historical circumstance it got called "pseudo killer whale". Oh well.
Take some law, like Newton's second law:
$$ F = ma $$
This only holds in an inertial frame of reference, that is one that is not accelerating or rotating. By convention, most laws of mechanics are phrased in an intertial frame of reference because it eliminates complicating variables like:


*

*How fast is the merry-go-round spinning?

*How far from the center are you?

*Is it spinning at a constant or variable rate?


There are other forces that aren't in that equation, like gravity. If you hold a ball in front of you and release it, it doesn't stay put: it falls to the ground. It falls because the force of gravity accelerates it downwards at 9.8 m/s2. We understand that when things are near a massive object, we must add a "gravity force" to our calculations to accurately predict what happens.
When things are spinning or accelerating, we likewise must add a "centrifugal force" to the calculations. "Pseudo forces" or "fictitious forces" is the name for a category of forces that must be added in non-inertial reference frames. Don't worry about the name "pseudo force" any more than a biologist worries about the name "pseudo killer whale". They are forces, demonstrable by experiment, just like other forces like gravity.
A: 
If centrifugal force isn't real then why am I being pushed on a merry go rournd?

It is not you who are accelerating outwards away from the car seat or the merry-go-round - it is the car seat or merry-go-round that accelerates away underneath you.
And as it moves away underneath you, the car's door or merry-go-round's rail soon bumps into you and pulls you along. This constant inwards pull is what makes you move around the circle.


*

*Think of you pulling the duvet away from underneath the plates, glasses and cutlery on a small dinner table. Everything stays where it is, but the duvet moves away.


From the perspective of the duvet (if you placed a camera on the duvet), though, it looks like it is the cutlery, plates and glasses that are moving away. But we know that isn't true; that is just an illusion. If you were that glass and all you could see around you was the duvet, then your brain would easily trick you into thinking that you are the one moving rather than the duvet. It is a typical optical illusion.


*

*Another example: imagine standing in a bus while wearing roller skates. When the bus brakes and decelerates, you feel like falling/rolling forwards. But nothing is pushing you forwards. It is rather the bus around you and underneath you, which is being pushed backwards. Your body just continues ahead with the speed it has until you hit something. If you look outside at the ground, it doesn't look like you are pushed forward - but when you look at the bus around you, it does look like you are thrown forward. It is nothing but an illusion.


So, all this is actually quite simple. You are not accelerating out of or pushed out of the circle - your body is merely continuing with whichever speed it has at the moment. If you have a speed directed tangentially to a circle, then you are naturally moving out of that circle. Only if that circle holds on to you - like the merry-go-round rail - you will move in a circular path because it constantly pulls you back in and avoids that you fly out of the circle.
In short: There is a centre-directed force due to the car door or merry-go-round rail, which pulls you inwards (we call this a centripetal force). But there is no force pulling you outwards. This feeling of falling outwards can be called a centrifugal effect or so if you will - but avoid the term centrifugal force, because it really isn't a force.
Now, regarding your teacher talking about inertial frames of reference
From the duvet and bus examples above, it is clear that depending on from where you are standing and watching, it looks different - a camera on the bus or on the duvet sees you throw forwards, while a camera at the bus stop or at the table sees you with no change in motion (you either keep standing still on the table of keep continuing with your speed in the bus).
So the point, from where we look makes a big difference. We call this point a reference frame. And if you look at the two examples again, it seems that whenever the reference frame is accelerating (the pulled duvet, the braking bus, the turning car, the turning merry-go-roung), then this illusion appears.
So, in order to avoid this illusion, people in the past have invented the term inertial reference frame. We call a reference frame inertial, if it does not accelerate. Only then do we not see any illusions, and only then do Newton's laws hold true.
A: In a non-accelerating frame (inertial frame) there is no centrifugal force. However, the centrifugal force is a real force for someone in a rotating reference frame (as you have discussed). Teachers who say it is not a real force are either being misleading or just want to educate new physics students on the role of centripetal forces without bringing in the confusion of the centrifugal force. Some problems are better solved in a rotating frame, and you have to account for the centrifugal force. It cannot be ignored.
Now, if you want to understand how the centrifugal force relates to the inertial frame, you just have to understand that your velocity is always tangent to the path you are taking (this is a qualitative, looser explanation for this phenomenon). For example, let's say you are on the right side of the car and it turns left. When you are turning, your body still "wants" to go in the direction you were moving before the turn. Therefore, you feel pushed towards the window, since your body still "wants" to be going down the road.
A: If you think about the car scenario, there are two possible scenarios.
1) The turn is very small, friction will provide enough centripetal force which is equal to centrifugal force (outward force) and you will stay still.
2) The turn has a high curvature. Then the friction will not be enough to match the centrifugal force which pulls you out. That's why you will get some support from car interior or you will hold the from seat to avoid you pulling out. With that extra force, you make centripetal force equal to the centrifugal force.
It is a pseudo force because it will be only felt by the objects which are in the same inertial reference frame.
Similarly in above scenario, if you are inside the car you will feel the centrifugal force (Because you are now in the rotating reference frame of the car).
But if you are outside the car you will feel nothing.   
A: Centrifugal force is not real in the sense that you observe it when you are in an non inertial systems, in which you see forces with no origin. This force is actually either friction from the floor or the normal the car exerts on you on the marry go around. 
