Is growth a necessity in capitalist economies?

What they probably mean (and confuse with free market capitalism in general) is that a fractional reserve banking system has to keep creating new money, and the economy has to keep up with that monetary growth or the system collapses. (The Crash Course preaches some of that stuff, I forget which chapter.) This is not a problem with “capitalism” itself but with our particular ponzi-scheme of government-monopoly fiat money. As Autolykos said, economic growth is simply growth in productivity, it does not follow that resources are ‘used up’ at a greater pace. I fact, resources are not finite at all. Higher productivity is another way of saying that we created more resources. The problem is in fact the opposite of what environmental socialists (read as in ‘national socialist’) want us to believe. We have to keep renewing resources through economic growth to run a sustainable economy. Their retreat into “renewability” and economic stagnation (“stability”) is truly unsustainable. This finite-earther stuff is dangerous religious nonsense. What these ascetics have a problem with is wealth creation, exploiting the earth to make humans better off. They are simply rich kids who are perfectly willing to give up (other peoples) material well-being for the sake of a spiritual notion. And this whole movement is kept together by communist and anti-liberal propaganda.