It is due to the slipperiness of the paper and the type of writing instrument you are using. It is frequently caused by oil from skin, clothing, etc. getting on the paper (and it might not even be visible) or may be caused by a flaw in the manufacturing (paper cannot be too smooth, or you cannot write upon it, as you say, or it might not take ink in a printing process).
With a ball point pen, especially a cheap one, the paper becomes so slippery that the friction of the ball in the penpoint against the paper is less than the friction of the ball against the socket of the penpoint. Accordingly, the ball “freezes up,” does not rotate, and no new ink is carried out of the ink cartridge to mark the paper, rather, the ball just slides across the paper.
The same can occur with a pencil if the paper becomes so smooth it does not overcome the cohesiveness of the graphite particles and no graphite is rubbed off of the pencil.
Other writing methods, like printing, fountain pens, markers, etc. might succeed because they do not require friction for their process. However, if the paper is so smooth, or has lost absorbency from absorbing the oil or other substance, the paper may not be able to “take” the ink, and the writing process will either be unsuccessful or will readily smear.
Left handers who rest their hand on the paper are more prone to this, presumably people with oilier skin would also be more susceptible.