In most stories, a good antagonist will make or break it. Whether the main character is fighting against a lie that he believes about himself or the world (a man/woman who learned better story) or a classic adventure story with a villain like Darth Vader, villains are important.
It takes a good storyteller to make us sympathize with the villain. It takes an even better one to let the hero die and the villain live, without feeling cheated. Lin-Manuel Miranda did both when he pitted Alexander Hamilton and Aaron Burr against each other both personally and professionally.
Hamilton and Burr reflect each other.
A story where the antagonist and protagonist feel disconnected is awkward. No, you don’t need to do the “mentor turns villain” cliche, but craft their characters side by side. In this case, both Hamilton and Burr wanted more. Both were both incredibly ambitious. Both of them were devoted to their families (proof: Dear Theodosia.) The difference was their core personalities and the way they were willing to go about it. That difference proved to be deadly. I’ve seen MBTI typings where Hamilton is ENTP and Burr is INTJ, which might explain some of their differences.
Burr wants to wait for things to come to him, stay in the shadows and not stick his neck out too far. (Come on, he had an entire solo called Wait for It.) By contrast, Hamilton stuck his neck out like a giraffe and was busy standing in the spotlight waving his arms to get attention for his wants.
The tables are turned.
While you don’t want reader whiplash, people aka characters need to change. Burr was like some of us: his temper moved at a slow boil. But once it got to a certain temperature, he exploded. After all the years of Hamilton beating him to the draw professionally, Burr had had enough.
Hamilton spent his whole life grabbing for things, but after an affair with Maria Reynolds and the death of his son, he was more willing to wait instead of jump. Both personal changes make sense, but it becomes heartbreaking in the end.
We can empathize with the antagonist.
This is one of the biggest points for every antagonist ever. You can tell if it’s a good book if the morals are the only thing delineating protagonist from antagonist. That being said, you never want readers to root for an antagonist, but that scary moment of “Oh. If I were in their shoes…I might be the same” is perfect for a villain. How would I react if one of my colleagues, someone who used to want me to mentor them, had cheated me out of everything I wanted professionally, not wanting to admit that it was partially due to my own approach? I don’t know. I can’t say.