Try to come up with a set non-colinear points where NO line passes through two and ONLY TWO points and you'll see the value of the statement.

You may think "I'm sure I can arrange these points in a way where EVERY line will cross three or more points" but you will fail if you try unless ALL points are colinear.

This is true for finite sets. For infinite sets, the Sierpinski triangle is a counterexample.