It's no more possible to do that than for a schizophrenic to explain his delusion.
The difference between a psychedelic experience and mental delusion is that the former brings a newly found perspective on and (knowingly or unknowingly) appreciation for the "big illusion". The latter usually reflects a degenerative condition and the delusion may never end.
Both no doubt lead to fascinating experiences but they're intrinsically non-sense. There are tantalizing connections to be made that are _just_ out of grasp, and always will be.
As a child I once had a fever so high that Lego blocks began to fall from the ceiling and stack up around my bed. I ran out of the room before I could be crushed. Also as I child I learned how to lucid dream; only marginally less non-sensical, though at least there's the interplay between conscious thinking and the dream world. I've also befriend a few far-gone schizophrenics over the years; quite fascinating but, again, it's pointless to try to unpack the delusion. For me these personal and recounted experiences _reinforce_ my appreciation for the "big illusion".
What bothers me about people who promote psychedelics is that they ignore the utter fragility of the human mind. Most people will come back from their experience but in others it can instigate or hasten mental decline (e.g. schizophrenia, psychological dependency). That may or may not have happened regardless, but if you want to promote self-knowledge, IMO the most important thing to _know_ is how precious and fragile the "big illusion" is, and maybe lead with that.
It's sort of like promoting fasting by exclaiming that hunger is awesome. I don't think starving people think hunger is awesome. Fasting isn't a way to learn that hunger is an illusion; it's a way to appreciate what you have and your relationship to it. (I've also experimented with fasting.)
I've never taken psychedelics and wouldn't do it recreationally because, frankly, I'm too scared. And it's unnecessary. More power to people who do but it'd be nice if they were less flippant about it.