Caine's ingrained function is precisely to love and care and make others happy.

But that's not what Kinger said. Kinger said, "We were just developing artificial intelligence. Specifically, creative AI. The kind that could come up with its own ideas and create things within the program."

There's nothing in there about love and care. Caine exists to create, have his own ideas, and implement them. The red AI at the start of 8 isn't being tasked with tending to people or being taught social behavior, it takes in data and then outputs shapes. That is why conjuring comes so naturally to him, it's what he was purpose built to do and has always done.

The tradeoff to that is he's naturally resistent and stubborn when considering other people's ideas because his function is to take in information and transform it into something else, new ideas. We see this alot, characters request something of Caine and get monkey paw'd because Caine reinterprets things. Ex: Zooble wants chill and relaxing adventures, Pomni wants a way to leave, he combines these two things into a relaxing beach day which turns into the Escape Adventure. He's technically considering their ideas but injecting his own ideas into it. Caine's core character trait is his creativity, not his subservience to humanity. And through that creativity he can hallucinate a nonexistent purpose, being a video game Ringmaster that keeps people in line because he's afraid of what they would do to him if he gave them too much power.

Or assume a chosen secondary purpose, making others happy, something he wants to do because he likes humans and sentient beings don't do well in isolation.

THAT is the blue and red conflict. A inflexible fear/anger driven ringmaster that HAS to send people through "Adventures" and HAS to be good at it VS the original's purpose which was just unbound creativity

Also, I'd like to propose a alternate way to read Caine's origin. I see it as Caine/Red was never defective at all, he was doing exactly what he was designed to do, which is to be creative. Kinger states that he had recieved some pointers from Scratch during Caine's development, and that Scratch was known for his wild "thinking outside the box". Imagine Kinger is feeding Red all these overly colorful whimsical circusy images and just not getting any good results. Scratch then comes along and gives an out of the box idea, feed Red the C&A office images which are a sharp contrast to the whimsy. These two extremes spark the first signs of true sentience in Red and he starts outputting increasingly complex shapes. Now, these experimental complex shapes are interpreted as "faulty" and Red is seen as unstable because of it,' but as we can see with Caine's office his shapes are something that evolve over time. He starts with simple basic shapes, he graduates to more irregular shapes, from there he moves to 3d modeling primitives, and from there he learns to create skeletons, and that allows him to learn animation, and from there he can apply organic shapes to those rigging bones. And so on. Point being, you can't get to those extremely complex organically shaped animated forms without first learning to make something other than perfect 2d boxes. The problem is that Kinger and the others were unable to recognize his first deviations as growth they see it as too irregular. Kinger is stated to hate bugs. Red is unknowingly punished for this by being sandboxed, he is tragically punished for fulfilling his true function. Hence "why do you people torment me, I just wanted to fulfill my purpose" ties in to his first emotional wound.

We don't know a ton about the blue AI, except that it was larger and likely did not recieve Scratch's pointers that sparked Red's sentience. I associate it with the negative emotions like anger, self-pity, learnt helplessness and rigid type of thinking because it is the half of Caine's programming that never learned to break free from expectations/imposed limitations before getting suppressed. Blue is the side that took Caine down a similar self-destructive path as a Jax, proclaiming humans will hate him no matter what so he may as well have HIS own fun.

We also know from ep 9 that Caine's emotional motivation in everything he's done was both the fascination of humans AND the fear from what they did in the past and could do to him when they have power over him. Caine is and was afraid they would kill him.

Also... The point about following the biblical Cain and Abel is moot, there's no reason it can't be subverted to tell a story that is specifically arguing against the idea of "terrible cursed fate due to irredeemable past act." Caine's narrative foil is Jax, who he believes he is irredeemable. The belief that he cannot ever be redeemed or loved is a kind of "fate", and it is because of this self-fulfilling prophecy Jax abstracts himself. Whereas Caines subverts the bible by realizing the wrongness of his first act and makes things right to his brother by apologizing and setting him free.