You know that all sounds logical, but consider this -
Upon closer inspection, Dr. Matoi didn't invent the scissor blade at all, according to the first part of the series. I'm not sure who invented it, or for what purpose, but it wasn't him. The only thing he invented was the Kamui, which he created to thwart the ambitions of the Kiryuins. The scissor blade was a weapon that belonged to his killer, and Ryuko took half of the scissor blade to help track down it's original owner. This is stated multiple times in the first arc of the show.
However later it's retconned so that Dr. Matoi invented the Scissor Blade to cut life fibres AND the Kamui as well. It all gets a bit convoluted.
Please don't make me dig up the screen caps to prove this, I'm too lazy. Just accept it as gospel truth!