Compelling villains are written with a deeper motivation for their actions than just 'hurt people' or 'be evil' and they have a tendency to challenge the status quo in some way. Such villains become sympathetic because the current status quo is oppressive.
It must be very difficult to write a villain for a contemporary piece of media because they can very quickly become a hero of the people.
You can always fish out of water a villain. Their solution could sound reasonable where they come from, but during the quest for enlightenment be made clearly wrong, and they refuse to change. Breaking that step can turn the audience.