Considering how much of an impact Hojo had on pretty much everything that happens in the game, it's strange that we don't really know more of what his real reasons were.
This is because Hojo is actually a fairly disappointing character.
The problem with Hojo (as a character, not as a human being; that’s an entirely different dissertation lol) is that he has so much potential for depth, but every time the canon creators get their hands on him they’re like, “Yep, he’s mad, that’s it. Nope, that’s his sole motivation. Science. No, there’s nothing deeper beneath that.”
“Oh, but look right there— He just had depth for a second!”
“Nope, that was a translation error, sorry. Just crazy.”
“Oh…”
So if you want to find anything satisfying in Hojo as a character, you really need to look into fanworks and headcanons. Canon will disappoint you again and again.
And really, for Hojo at least, I’m fine with that. I not-so-humbly think the Hojo of my headcanon is a way deeper and more complex character than the canon Hojo, anyway.
So the Hojo of my headcanon? Suffers from a lifetime of feeling powerless for being a wimpy and unlikeable dude. He’s not one to adopt the adage “If you can’t beat ‘em, join ‘em”— he’s more likely to take the adage, “If you can’t join ‘em, beat ‘em.” So a history of social rejection (from his peers, from his parents, from romantic prospects, from fellows in his career, from all of or a combination of the above??) led to him ceasing to try to gain that acceptance and instead turned him down the path of vowing to prove everyone wrong about him.
Like, when he was in school he probably dealt with not being invited to any parties by insisting that parties were stupid and he had more important things to do like study science and also work on pretty crazy experiments that were dangerous and unethical but also won him international first place in the science fair or something. Meanwhile the people not inviting him to parties are just trying to get to third base.
Anyway, in that light all his actions take on this hue of defensiveness and denial and trying to attain a much more vulnerable personal goal even while he just tries to insist his entire life that he doesn’t care about any of it at all because he’s stronger than that. Better than that. He’s better and smarter than everyone, and he’ll
prove that to them, and also that he doesn’t feel anything about it. He’ll prove that, too.
I guess the intended point is that he though the outcome would help Shinra corporation, and thereby benefit humanity somehow in the long run.
I don't think that was ever implied in Hojo's motivations at all, although for what it's worth I do think those were Lucrecia's motivations.
And as for these tired arguments, which I want to bang my head against a wall every time I read every few years:
"Maybe Hojo isn't Sephiroth's father."
He is. Get used to it.
"But ewww, I don't want to think of Lucrecia banging Hojo, he's so ugly and gross."
She did. Get used to it.
Also, they were canonically married, and also aside from DoC's shitty portrayal of Hojo we have no basis to say he was ugly or gross in his youth.
Also probably none of your business who she or anyone else decides to sleep with.
"Lucrecia was Hojo's research assistant!"
Lucrecia was a fucking "Class A Biotechnologist" and had the title of "Doctor." "Research assistant" my ass. Respect that woman's authoritah. (Spoiler alert: Not all the women working in hospitals are nurses or secretaries, either.)
"I liked Lucrecia's original representation better, when she was less pretty."
Lucrecia's original representation was this:
We have absolutely no idea how pretty she was or was not. Whatever you thought she looked like before DoC, either you imaged or someone else did and then drew it for you.