I just had a thought... Maybe one of the conditions required to achieve a natural 5th evolution, or at least in the way that the big three did it, is to separate yourself from, or perhaps reject, either your monster parents or the apostles, making them transcend their status as a superhuman, at least in the way the rest are.
I don't have much to support this off the top of my head, but the big three were mentioned to be aberrations that shouldn't exist. If we consider that from the point of what seems to be the purpose of superhumans, aka potential vessels for the apostles, someone who's disconnected themselves from both the apostles and the limitations placed on them from being such a potential vessel would certainly be that.
In particular, I remember a line about Henry having rejected his origin, or something like that. I don't remember it well though, so I might be wrong.
This theory also fits with what the judge in the truth dream said to MC: "Until cleaved from mother and father, thyself remaineth unwhole". Since the fifth evolution is often associated with being complete, that could be what he was reffering to. Seperating yourself from the apostles, which in a way are the source of your power, is the only way to make your "self" become "whole".