"Just because a study doesn't replicate, doesn't make it false."
This is a subtle point, but truth or falsity isn't really the issue. The problem with a non-replicable study is that the rest of science can't build on it. You can't build your PhD on top of a handful of studies that turn out to be non-replicable, and so on. It is true you can't build science on outright false statements, either, but true statements that aren't adequately reproducible are also not a solid enough foundation. That may seem counterintuitive, but it comes down to this truth not being binary; even if a study comes to a nominally true conclusion it still matters if it didn't do it via the correct method, or is somehow otherwise deficient in the path it took to get there. Studies are more than just the headline result in the abstract.
But the whole process of science right now is based on building up over time. How could it not be? It has to be, of course. But non-replicable studies mean that the things you're trying to build on them are non-replicable too. It doesn't take all that much before you're just operating in a realm of flights of fancy where you may "feel" like you're on solid ground because of all the Science you're sitting on top of, but it's all just so much air.
However, it is also true that non-replicability is a signal of falsity, and that is simply due to the fact that the vast, vast, vast, exponential majority of all possible hypotheses are false. As is another subtle point, a scientist engaging in science properly should probably not come to that conclusion and may not want to change their priors about something because of a non-reproducible study very much, but externally, from the generalized perspective of "what is true and is not true" where science is merely one particularly useful tool and not the final arbiter, I may be justified in taking non-replicable studies and updating my priors to increase the odds of the hypothesis being false. After all, at the very least, a non-replicable study tends to put an upper bound on the ability of the hypothesis to be true (e.g., if someone studies whether or not substance X kills bacteria Y, and it turns out not to reproduce very well, the lack of reproducibility does fairly strongly establish it can't be that lethal).