This is a question I’ve thought about a lot, and one that many other people have also thought about a lot and procured many answers, most of which are good – all of the ones I’ve heard have been good answers, at any rate.
And while I’d love to say that I, as an authority on villains, have the answer…my conclusion is that I just have a lot of good answers and good thoughts that are refutable in such a way as to spark a lively debate about it, and thus I’ve drawn a different conclusion.
Whether or not there is one single complete and objectively correct answer to this question, what’s more important is that you have your own answer to this question, and that you know it and are solid on it before you write. This will help keep you from conflating villains and antagonists, recognize when you’re writing a mere antagonist, and not call them a villain or force them to be something they’re not. And it’s okay if you have an answer where others might disagree. I mean, look at Snape! Is he a villain, an antihero, a misunderstsood hero?
People hold all of those opinions and more of him, and they are often quite strongly held. What causes a person to view Snape where they do on the spectrum of good and evil seems to depend on two factors: one, how well they understand his character and simultaneously remember all the things he did and said, and two, where they place moral values. And a lot of people disagree with Rowling’s assessment of her own character, and that is entirely okay. Especially when everyone remembers that a writer’s own assessment of their own character is not always correct, or at least objective truth.
I think of my own current main character – I find him to be an endearing jerk. Other people might find him to be a selfish brat. I think they are wrong but that’s also my opinion; maybe they can’t stand sarcasm and sass and if that’s where they put their values, then yeah, he’s going to be much more insufferable. Just as in real life, not every person is going to like any other given person, in fictional life, characters who are rounded enough to be like real people will not be liked by every person, nor judged the same way.
So what makes a villain a villain? Think hard about that question, and then when you have your answer, run with it, and perhaps you’ll find that the dichotomies of good and evil upon which you have decided will help shape aspects of your plot, as well. Since part of that dichotomy for me is caring about other people, some of the important plot arcs for my heroes involve becoming more personable, more aware of others around them, and more willing to trust them, whereas the arcs for my villains sometimes tend more towards despondancy, willingness to sacrifice others for their (the villain’s) own goals, increased coldness. Maybe you’re the kind of person so jaded by the unkind and morons of our world that your definition doesn’t involve a dichotomy of love for others or not. We all know how hard it is to label people because they’re dynamic, but it’s also because all our labels are different, too. Don’t worry about whether your definition is right or wrong, but just if it makes sense to you.
Of course, keeping an open mind, a flexible definition, that grows as you learn about the perspective of others is not a bad idea either. Either way, even if your definition changes later, you should at least have one so when you write a villain, you know what you’re writing in the first place.