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Why does the friction of a solid sphere (while rotating and moving) has to be static and not kinetic ,not to slide?

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The difference between static and kinetic friction depends on the relative motion between the two surfaces in question. Therefore, if the ball is slipping while rolling then kinetic friction must be at play.

However, if the ball is rolling without slipping and experiencing angular acceleration, then static friction is at play because at the point of contact the two surfaces are not moving relative to each other. This is because in the frame of the surface that the ball is rolling on, the linear velocity of the bottom of the ball is equal and opposite to the velocity of the ball across the surface itself. Hence the bottom point of the ball will have a velocity of 0, and there is no relative motion between the ball and the surface.

If the ball is rolling without slipping and moving at a constant velocity then there is no friction at play, similar to how a book laying on a table does not experience a static friction force even though it is not moving.

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