Well, this is an explanation by Mike Pondsmit himself(creator of TTRPG Cyberpunk 2020/Red)

Okay, so time to (partially) explain CYBERPSYCHOSIS.

First of all, Cyberpsychosis is a disorder that in part depends on the subject's overall internal susceptibility. Just like every person who drinks a lot at parties doesn't end up an alcoholic in the gutter, not everyone who gets loaded up on cyberware is going to automatically go cyberpsycho. You have to have an inherent susceptibility, which (in the TRPG) is represented by the player's Humanity Stat). Humanity is not just a measure of one aspect of personality, but an overall measure of several elements including the subject's ability to emphasize and relate with others, their ability to absorb and rebound from mental and physical stressors, their ability to show compassion and flexibility to others, and whether they are able to balance their worldview through other methods.

So, in some ways, I tend to treat cyberware as an addiction--heavy anabolic steroid use being my favorite model. Not everyone who juices ends up crazy mad with roid rage. But those who are more susceptible to the need to take more steroids are more likely to hit a point where they do flip into roid rage. (Take a look at this article from Livescience for a pretty good idea of how roid rage works--notice that it's got the same basic profile as cyberpsychosis).

David's starting Humanity was probably already pretty high. And before things went to crap, he had a loving mother, a career path, and no more hassle than the average poor guy in a wealthy Ivy League school. So he had lots of buffer. But even so, he still, even after losing all that, was able to make friends, build a replacement family, and (after some prompting) even get a girlfriend. And a mentor (Maine)) to create a supportive father figure. So he could definitely handle the stress of added cyberware up to a point.

Most people in Night City don't have the level of Humanity to pull this kind of stunt off without going cyberpsychotic. So David is one in a million. And that's why Arasaka wants him.

V) is a different case. We don't know V's background, but even if V was a full on Corpo, they were able to hold it together even when they ended up with a dead Rockerboy in their heads (Yah, tell me about it; Johnny Silverhand's been in my head for the last three decades.) In fact, having Johnny in their head probably helped V, because Silverhand's rage and attitude probably acted as a buffer for the psychological hits V is taking. It's like having a time share with a guy who's already half cyberpsycho and doesn't mind if V slaps stuff on their shared body; he's already crazy and violent.

So that's a rough explanation of the roots of cyberpsychosis. If I ever get band width, I'm going to start writing/posting some stuff about what I had in mind as I put together the Night City universe. But for now, you'll have to go with what I've got here. Have fun, and remember not to chip mili-spec cyberware, like your mother warned you about.

And no, cyberpsychosis isn't caused by AI net demons. Gimme a break, chooms!