How does friction helps us to move/walk? We all know that it is friction which helps us to walk on any surface. If there were no friction we could not walk or might walk but very slowly. According to Newton's 3rd law, if we apply an oblique force on a smooth surface the surface should also exert an opposite force on us. Then how does smooth surfaces obstructs us to move forward or atleast slows down our speed?
Is it that the atoms/molecules/particles remain arranged so uniformly that the force applied on the surface gets distributed equall in all directions which eventually results in the exertion of a vertical force on the body? Whereas in case of rough surfaces the partixles remain arranged non-uniformly and thus exert force exactle in the opposite direction of the force applied on the surface.
Is this intuition correct?
I illustrated my intuition in the image below.

 A: 
According to Newton's 3rd law, if we apply an oblique force on a smooth surface the surface should also exert an opposite force on us.

The thing is, while we are moving we don't push ourselves forward but we push the earth backwards. Think of it like you are lying on the ground and pulling a branch on the ground to move towards it. What you are actually doing is applying a force on the branch so that it's reaction force will push you along the direction that you would like to go. Once you understand this, think about people's feet or car wheels. Note that they push the ground backwards almost like a rower pushing the sea backwards. If you are walking to the North, your feet would move to the South while they are on the ground. While they are moving to the North they are on the air and don't actually exert a force on anything. Similarly the bits of a car wheel which are in contact with the road goes backwards.
On a smooth surface your feet can't exert a horizontal force on it simply because they are sliding on said surface. Whereas on a rough surface it is easy to push the surface horizontally.
