Loki’s central motivation is his desire to do what is right. To do his duty.
(Sometimes, of course, he is wrong about what is right. Well, okay, he was wrong once onscreen, when he tried to destroy Jotunheim.)
Winning the love and respect of his father and brother is his secondary goal.
The reason he failed to achieve his secondary goal is that he tried to win their love by doing what was right. Odin and Thor are both thoroughly evil people, so the nobler Loki became, the more Odin and Thor detested him.
At the end of his first movie, Loki realized that the only way he could possibly (but probably wouldn’t) win their affection was by becoming evil like them.
And he made his choice. Loki decided that he would rather have his father and brother disown him, physically torment him, and attempt to murder him – all of which did indeed happen onscreen, btw – than become evil.