You're talking about his motivation, his fixation with Superman, and that's a part of the problem with the character, as his motives and enmity with Superman have always been vaguely defined and/or unconvincing.
He is a 12th or 14th level intellect devoted to amassing more knowledge, or is he a Space-Pirate? Does he see Superman as 'the great architect' his creator, Or is he obsessed with Superman as he is the last Kryptonian and Brainiac has to have him to go along with Kandor?
Successive writers have tried to come up with the best rationale for him, why it is he gravitates towards Superman constantly, but outside of an obsessive compulsion that mirrors Lex Luthor's own pathological fixation with him nothing quite sticks with Brainiac. He has the entire Universe to explore and play in, and yet keeps bothering Superman on earth...?
Maybe he was created to be the protector of Krypton, so maybe should be seen as being much more advanced eradicator?