Explain why a line can never intersect a plane in exactly two points.

So, this is kind of a hard concept to explain without any pictures, but I'll try anyways.

Think of a plane as like a sheet of paper, and a line as a metal rod.
If I want to intersect the plane, it means that my line (rod) has to touch the plane (paper).

If I poke the rod through the paper, it only intersects it in one place, and I cannot fold or warp the paper to change that.

The only other way I can make these two touch is if I lay the rod on top of the paper. However, when I do this the paper is touching every single point along the rod...

I hope this kinda helps explain why you can never intersect in exactly two points.