Why should you focus on creating likeable antagonists? Because it becomes boring for your audience if you don’t. If there is nothing to like about your antagonists, your antagonists will be “one note” and two dimensional.
So how do you write likeable antagonists?
You should base your antagonist’s actions in logic. The evil for evil sake antagonist becomes silly and unbelievable. It should be easy to rewrite your story and make your antagonist into the protagonist. Their actions should drive their story forward and be based on a believable goal. In this way your audience will be able to relate to your antagonist. Being able to relate to someone is the first step in finding them likeable.
Your antagonist should be the hero of their own story. If we look at Marvel’s Avenger Movie Infinity War. Thanos wants to wipe out half the population in the Universe. He believes that the Universe is dying due to over population driving starvation and war. He sees his actions as a kindness, he believes it is something that people don’t want, but need.
There is a book called “Save the Cat”. It is a book that has a method developing screenplays. I am not a fan or follower of such books. But this book gets it name from the concept of writing a likeable antagonist. Your villain can be save evil as you want. But if he saves the cat, people will like him. By doing something like saving a cat, the most evil person will demonstrate some redeemable feature.
The other way to get people to like someone they should hate is to make them really good at their job. The creature from the Alien movies is popular because it is an amazing monster. Hans Gruber in Die Hard is a great bad guy. He is really good at his job. He has planned everything, even the involvement of the FBI. The ultimate version of this is Walter White from Breaking Bad. He become a horrible person, but he is really good at making Meth.
Give them a back story. If a person is bad now, perhaps it is conditioning. Perhaps they have been forced to react this way. It has become who they are. This is a tragic character. We like them as much as pity them.
How a character acts and reacts will impact on how the audience relates to them. Making their action real and logic is a must. Check out “Writing Screenplays with Intelligence” for some great tools.