That is an interesting argument, but where is the proof? Economics is a very murky “science” as it is, a broad statement such as “capitalism is inherently unstable” needs some healthy data backing it up.
The same argument could be made about communism, as an economic system it doesn’t have the best track record.
Socialism seems to have a pretty good track record. But even in socialism there are issues, especially around ensuring a steady supply of kids coming through, once population starts falling the cracks start appearing.