Each pair forms up only one possible diameter when points are located at strictly opposite sides.

If we are considering "at most" extreme case then all ponts should be evenly distributed on the circumference of the circle, and since we have 17 points, only 16 out of 17 can be placed opposite each other and 17th one would not have a pair.

So there should be 8 possible diameteres at most however if we assume that there could be an overlap, then 17th point can overlap to any other and form up another 9th diameter.

OR maybe some more tricker logic lies behind the correct reasoning of subject problem