I don't. I'm simply restating what seems to be general consensus amongst both users and mental health professionals. Actual data is hard to come by, since actual research has only recently begun to happen.

At this point though, any assertion that psychedelics cause anything more than a very slight increase in the background rates of diseases like schizophrenia would need a serious amount of evidence to back it up. Psychedelic use is common; something like 15—20% of the American population tries them in their life. And the general understanding of diseases like schizophrenia right now involves actual structural changes that simply aren't plausible consequences of infrequent psychedelic use. I won't speak toward long-term, frequent use, but by all the evidence I've personally seen, LSD in particular is extraordinarily safe for the population of people without a family history of schizophrenia.

I'd also like to point out that the original assertion—that psychedelics trigger psychotic breaks—itself doesn't come along with that much in the way of evidence. The original notion came about in the '70s when mental health professionals started seeing a higher proportion of their patents coming in after having tried psychedelics. I'm not sure if hard data was collected (or at least, I haven't been able to find any), but the most straightforward explanation for this is that this likely simply mirrored the increase in the background rate of people using psychedelics. If the background rate went from 1:10 to 2:10, then you'd expect that the number of people coming in with mental health issues will show a doubling in psychedelic usage rates. And in the fifty years since then, I've not seen much additional evidence for a causal link between the two.