Why is this definitely true? Other economic/societal systems have fallen in the past. Why does that mean this one has to? Or is there some other reason why this statement is true?
I'm not trying to cast doubt upon this idea. I'm just trying to find out its justification, from a scientific perspective.
Cheers.
The capitalist mode of production has been incredibly powerful at orienting human systems toward commodity production. It incentives it's own continued existence. However, it also creates contradictions.
One of the contradictions is between labor and capital. This contradiction could end the system "internally" if labor is triumphant over capital (creating the conditions for socialism). This is the contradiction Marxist have primarily focused on. At points in history, it seemed like this contradiction would inevitably destroy capitalism.
Another contradiction is between capitalism and the environment. Capitalism in its pursuit of profit demands ever greater exploitation of the natural world, greater exploitation of labor (see above contradiction) and ever greater numbers of consumers to purchase it's commodities. Capital, for the time being, has succeeded in increasingly exploiting labor and finding consumer markets. However in climate change and mass extinction, we're seeing something capital can't contend with. The time and spatial scale it's occuring over is beyond the ability of "capitalist central planners" to deal with.
There are some who think these contradictions aren't so severe. For example, most liberal environmental advocates (e.g. Dr Michael Mann of Penn State) believe that climate change can be responded to effectively within the current system. They point to things like the lower cost of renewables vs fossil fuels as evidence and do not think any kind of degrowth or system change will be necessary to contend with climate change. In fact, some argue that advocating for degrowth or system chagne undermines the climate movement. These types also tend to focus on what climate change does to the west and deemphasize global south nations.
Given the under-promising and under-delivering that we've seen from the wealthy nations of the global north at events like COP26, I'm very skeptical of the liberal climate activists' stance. I suspect that if capitalism survives the next century, it'll either be a capitalism on a very short leash and transitioning toward socialism, or it'll be fascism existing in the midst of the end of large scale civilization.