If I understand correctly, you're just basing that statement on climate change or war destroying us before we can do any better than Voyager, right? Because if we don't assume the destruction of humanity or the complete removal of our ability to make things leave Earth, then just based on "finite past vs. infinite future," it seems incredibly unlikely that we'd never be able to beat an extremely old project operating far beyond its designed scope.
Many reasons why. The probability is based on many many many factors. What you mentioned is just a fraction of the factors.
If we do ever reach that distance again it will be even less likely we do it for a third time.
I'm pretty bearish on human interstellar travel or even long-term settlement within our solar system but I wouldn't be so pessimistic on unmanned probes. The technical hurdles seem likely to be surmountable given decades or centuries. Economic growth is likely to continue so relative cost will continue to drop.
Absent a general decline in the capacity of our civilization the main hurdle I see is that the cost is paid by people who will not live to see the results of it but I don't think that rules it out, I'd certainly contribute to something like that.
What are some of the other factors you are thinking of?
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This is reflexive pessimism with no substance. You're not articulating a set of particular challenges that need to be navigated/overcome, which could provide a roadmap for a productive discussion; it's just doomposting/demoralization that contributes nothing.