Here's a different notion of how our economic system requires growth to function. Our system requires inflation to encourage people to spend and invest. In a deflationary environment, it's better just to hold onto money - in which case, the economy freezes up completely. Inflation has two different meanings that are of course related. One meaning is an overall increasing level of prices. Another meaning is an increasing money supply. If the supply of dollars goes up, then the value of each dollar goes down, which means prices go up.
Our economic system needs prices to go steadily up in order to encourage people to spend and invest, which is what keeps the economy functioning. Prices will go up as the money supply goes up. The money supply goes up as debt goes up. This is what a growing economy is. I.e., our economy indeed requires growth in order to function.