I'm not asking because I don't know why she's both a great character and sympathetic villain done right, but because I want to know what aspects made her that way when compared to the other villains in both Steven Universe and MLP, minus a few exceptions? What did most of those villains fail to do while Spinel succeeded in terms of being a sympathetic villain done right and why? Again, I just wanted to know.

Competence for one

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What do you mean?

First fight she takes out everyone with little effort

A legitimate reason to be upset would be another reason.

Spinel honestly believed she and Pink Diamond were best friends, and she dedicated her entire life to playing with Pink and making her happy in a way that only gems made for a purpose are capable of. In return, Pink not only didn't reciprocate those feelings (understandable, just because someone feels one way about you doesn't mean you need to return those feelings), but she never told her that. Instead she allows Spinel to believe that they were best friends. She then used Spinel's trust and tricked her into 'playing a game' that was really just an excuse to keep her in one place and make her stop bothering Pink. Spinel was then left in the garden to 'play' by Pink, who made no attempt to go back or tell anyone she was there, resulting in Spinel standing in place for 5,000+ years waiting for someone who was never going to come back.

While many would argue that jumping straight to planetary genocide is an extreme response to being abandoned by a friend, Spinel was also dealing with literal millennia of complete isolation and the mental trauma that causes. Finding out you were tricked and forgotten about by the most important person in your life after dealing with that is more than enough to cause anyone to have a psychotic breakdown and a desire for revenge. Spinel, being a gem created to always be happy and thus having no experience in negative emotions, thus reacts in the only way she can think of; by trying to destroy Earth and the Crystal Gems, which she sees as the things Pink abandoned her for. Destroying Earth hurts Pink in the same way Pink hurt her; destroying her world and taking away her happiness.