Why the friction is nil in rolling friction?

Friction is nil in pure rolling motion on a horizontal surface. Suppose friction were acting on a sphere in pure roll on a horizontal surface. If it's direction is such that it increase velocity of mass centre, it must be decreasing ang vel. But if it is such that it decreases the angle velocity, it must be increase velocity of mass centre. Either way you get a contradiction and you can't have friction in pure rolling motion on a horizontal surface. But suppose a sphere is in pure roll down the surface of an inclined plane. Then there is friction on the sphere directed upward along the plane of the incline.

Friction arises when two surfaces slips or tend to slip. So when body is in state of pure rolling the two surfaces are actually just became in contact and again loose it hence there is no friction observed.

Any plane surface, though looking plane, has a lot of microscopic ups and downs. when two plane surfaces are kept crossed opposed to each other for some time, the microscopic hills of one surface fit into the corresponding valley of other surface. when you try to displace one body over the other tangentially are working against the minute barrier hills, your force if sufficient to crush or uproot the hills, the object moves forward. The more rough a surface is the more hills and valleys, the more force required to break the hills, the more the friction.

concept of origin of frictional force. when you roll some spherical object, you help it climb those microscopic mountains. because when a sphere touches at a point on ground, that point of contact acts as fulcrum and the rest of the ball moves about fulcrum till a new fulcrum appears, so on. As you know, instead of pushing, if u use the methodology of fulcrum on any object, it will reduce your effort and energy required.