I think you are mistaking the fact that you can easily find an example satisfying the theorem’s statement with the proof that the statement is always true. Of course given any set of points that aren’t all on the same line, your nine your old could find a line passing through only two points. But could they explain to you why this is always possible, no matter the configuration of points? You can’t just say “I draw a line between two points and that’s it.” You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me).

His statement helped me. It's not that every three points are non-collinear, it's that any three points are non-collinear. A set of points all lying on a line is the only exception; you can have every point lying on a line except for one, or two, or whatever you want. In a square grid of sixteen points, there are lots of sets of four collinear points for example, but not all sixteen, and that's what counts.

So the theorem proves that no matter which way you arrange any finite set of points, except for all on the same line, then you can always find a line with exactly two points.