Why are there two pressures acting on a body in opposite direction during free fall on earth? 
This is how my sir explained this to me:
There are more than billions of atoms present in the earth's atmosphere. All those atoms have their force acting downwards.
When he explained this diagram to us, he said that pressure is a perpendicular force. So it also acts in upwards direction. I am not able to understand this. If all forces are acting downwards, how come atmospheric pressure in acting upwards as well as downwards?
I did not draw in the image another direction of pressure acting upwards from below because that was not the image in my mind but the one that I have drawn is.
I also agree with the point that gravity will also keep on decreasing as we go higher and higher.
My answer to this is that (please correct me if I am wrong):
If a body is going down, it exerts a force of its weight on air, therefore air exerts an equal and opposite force on it. But it is wrong since it should be a value of 1 atm and not the weight of the body.
Then, from top we can say that there is a force acting downwards on the body which is pushing it downwards and that is atmospheric pressure.
Please help me in understanding this.
 A: 
I did not draw in the image another direction of pressure acting upwards from below because that was not the image in my mind but the one that I have drawn is.

Your image in your mind is that pressure is a force which does not act upwards. That means that an object will experience an unbalanced downward force due to the atmospheric pressure of $14\text{ psi}$. This force will depend on the amount of surface area that is pointing upward. The more upward surface area the greater the pressure.
A simple experimental disproof of your theory is rather easy. Hold your hand flat with the palm facing upwards and the fingers together. Now, rotate your hand so that the palm is sideways. By doing so, you changed the upward surface area from about $35\text{ in}^2$ to about $5\text{ in}^2$. If your theory is correct there would be a difference in $30\text{ in}^2 \ 14\text{ psi}=420 \text{ lb}$ downward force. Since you do not feel that dramatic increase in force then you can be sure that the pressure does act upwards as well.
As a further exercise, consider also the forces exerted on a helium balloon. Could a helium balloon float if it were only pushed down with air pressure as you describe? Estimate the forces acting on the balloon according to your theory.

If a body is going down , it exerts a force of its weight on air , therefore air exerts an equal and opposite force on it.

You do have Newton’s 3rd law correct here, but not the magnitude of the force. The weight is a gravitational interaction between the object and the earth, it is not the air pressure. Since the object is moving the interaction with the air can be split into two parts: the buoyant force and the drag force. The buoyant force is the difference in the static pressure from the top to the bottom of the object. It is equal to the weight of the displaced air, not the weight of the object. The drag force is largely due to friction. As an object falls down, both of these forces point up. A balloon uses the buoyant force to float and a parachute uses the drag force to fall slowly.
A: Atmospheric pressure comes from air molecules bouncing of the object. As the molecues are moving in random directions, the average force  they exert is perpendicular to  the surface they are hitting. The total force on an object at rest in the air is therefore it's weight together with  the sum of the pressure forces. This sum is called  buoyancy, and is equal to the weight of the air which would be present  if the object were not there. We know this is so because, left to itself,  the air does not fall down. Once the object starts to fall then there is also air resistance, but there is no simple formula for air resistnce,
A: The atmospheric pressure — as the hydrostatic pressure — is caused by gravity, particularly  by weight of the air above a given point.
So someone my imagine it like this (gravity is nevertheless  downward force, isn't it?):

But it is not correct.
Atmospheric pressure works in all directions, so more realistic picture is like this one:

Now let's put a body between those different altitudes

and we may see that the upward pressure on the body not only exists, but it is even larger than the downward one.

But wait a moment... how gravity with its downward direction may cause an upward force?

*

*And what does gravity with a stone falling into water? It pushes some water upward.
Here are some other examples of how gravity pushes things upward:

