Say you've got a set of 5 points that are not all collinear (e.g. everytime you draw a line, you never get all 5 of them). Now every time you try to draw a line

Say you've got a set of 5 points that are not all collinear (e.g. everytime you draw a line, you never get all 5 of them). Now every time you try to draw a line between two points, you always end up with a third one. Can this happen? This is what is stated here: there always exists at least a pair where this does not happen.