I think Pink learned to appreciate others slowly.
Clearly she was overcooked like Amethyst, so she probably lacked a lot of the built-in programming she was supposed to have.
1) Because the other Diamonds were so restrained, she would have felt very different from them to the point of thinking her emotions themselves were different and lacked the close connection Steven had with the Crystal Gems.
2) Her Pearl was supposed to obey and keep her secrets, which would have lead her to believe that Volleyball was her only true friend. Damaging Volleyball taught her other beings have feelings other than Diamonds.
3) So she always treated Pearl gently. So Pearl wasn’t afraid to suggest breaking rules, teaching Pink that some Gems can change.
4) She became fascinated by organics and their ability to change and become better, which she wanted to keep for Pearl and herself. So the two of them pretended to be a rebellion so she could surrender to herself, but the Diamonds stepped in to fight the “war” for her. Because of poor communication, she didn’t understand they just didn’t want her to fail and lose faith in herself. The same thing the Crystal Gems would do with the fake test for Steven.
5) Ruby and Sapphire Fusing taught her any Gems could change, become better. So she made a real Rebellion, to tape into the potential Gems could have outside their roles and end the cultural and technological stagnation of the Empire (they could have developed robots and FTL anytime, but only did to compensate for Era 2 weaker Gems).
6) She screwed up faking her death, thinking the other Diamonds couldn’t love but could be taught fear, and by protecting them from Bismuth she lost another friend forever. But she found Amethyst, literally the reason it all happened because if she had emerged on time Pink never would have gone to see the organic life. Amethyst was basically a tiny version of Pink herself. She gave Amethyst the family she didn’t have.