Capitalism as an endless game
The first and most important argument is that capitalism is an economic growth system, but it has never historically included the factor of economic sustainability. It is not only capitalism, but also any political body that has as its leaders oligarchical few who profit from exploiting natural resources. That would include Communist nations as well, because although their propaganda says they are all about equality, there are certainly wealthy oligarchs who live a privileged life. In other words, the book opposes making money by exploiting natural resources or by ignoring adverse effects on the earth's ecology.
The negative effects on the environment
The book then elaborates what these negative effects actually are. Producing plastic and burning fossil fuels make the short list, of course, but also mining and logging. Certain kinds of mining do damage to ecological balances, say the authors, and so does logging. Lately, the burning of the Amazon rainforest might be worth mentioning here. In addition to these imbalances, there is the threat of approaching ecological tipping points when the chemical balances of nature might tip one way or another. There is the breathability of the air and the ozone to consider, and they mention that oxygen is made by trees; to remove trees from the earth is to slowly choke ourselves of air.
Wealth and power
Obviously, the science is long settled, and yet still there is serious resistance to ecological movements. The book mentions that wealthy people don't really think about life for common people that seriously, nor do they care about the future of the planet, because their lives are filled with pleasure, luxury, and power. The money gained by burning the Amazon, for instance, although it might seriously damage the earth's livability, prevents leaders from acting honestly. There is a thematic connection between the desire for wealth, the desire for political power, and a disregard of other people and of the future. In other words, the planet's leaders tend to be literally sociopathic. The call to action is a true resistance movement against the wealthy.