"Every villain is a hero in his own mind" ~Tom Hiddleston
Our entire lives we have been told one thing: There is good, and there is bad.
What we weren't told is that our thought process of good and evil is actually a varying gray scale.
The key to making a convincing villain, is giving them a justifiable reason for their actions. We don't have to like it, but there is rarely ever anyone who ever does something bad just for the sake of being bad.
Take Madelyn from my short story
What's coming, You don't realize that she's the villain from her point of view. But from the way Even and Teresa talk you begin to see that Madelyn isn't as innocent as she seems to be. She claims that she 'did it all' to protect them. Now while we don't know what Madelyn did, we certainly can imagine what it must have been to end with her being treated so harshly.
She had a reason for what she did, and while she was using a "the end justifies the means"philosophy, she has a valid point. How do you know that if the story was from Madelyn's point of view, we wouldn't say she was the hero?
Villains are heroes in their own mind. Madelyn believed that what she was doing was wrong, but that she was doing it for the right reasons. Take a closer look at many of the characters you know and love, many of the 'heroes' that our culture raises up actually believe the same thing at one time or another.
Writing isn't Protagonist verses Antagonist, its actually the Protagonist against another version of themselves. Thats what makes all the difference when it comes to the final count down. If the reader can see themselves becoming the villain then you've done your job. But there's one crucial thing that you have to remember: Every villain is a hero in their own minds.