Okay, I'm just going to start by explaining the difference between a "villain" and an "antagonist".
A villain is someone evil that actively opposes the good guys. An antagonist is someone that opposes the protagonist, but isn't necessarily evil.
It's important to make the distinction between the two when you're crafting a character. Traits should be given based on whether someone is evil, or just not on the same side at the main character. Someone at school that doesn't like your MC shouldn't be torturing people instead of doing an extracurricular, and I doubt the destroyer of mankind enjoys crocheting.
At the same time, neither of them should be flat characters. I don't think anyone is 100% evil. Unless they're mentally ill, they don't kill people just for fun. They have to have some sort of motivation. While the "they hated me so I'll show them hate" trope is overused, is generally works well as long as it's explained properly. Another fun one is, "I need revenge because they killed my parents and no one else will help me". There's a ton of different ones, and chances are you'll make your own.
They should also have goals, dreams, hopes, etcetera. They're not a robot (unless they are, I don't know your story!). Hobbies and activities are important, too. Maybe not something as peaceful as crochet, but maybe they like to build machines.
It's your villain, do with them what you will. Just keep in mind that they are a character, too, and deserve as much care as your MC.
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