Creating a Sympathetic Slasher Villain without Downplaying their Crimes

I feel like there's this tendency in the slasher genre that whenever they want to make the villain sympathetic, they try to water down their actions. For instance, they'll throw in an Asshole Victim so that we don't hate the killer too much or I've seen some cases where one of their killings is an accident. What I want to do is have a sympathetic serial killer, who at the end of the day is still a killer. So what makes a villain sympathetic, even when they're committing horrific murders?

Do you already have a villain planed out?

I have the basic outline: My villain is a serial killer. His backstory is that he's a former soldier who now works for a secret government agency as a Torture Technician. This will be used to explain how he's able to avoid the police. At the moment I have him being an introvert, but I feel like that's a bit of a cliche. I'm thinking of having him becoming more confident and social after he begins his killing spree.

Have you ever read The First Deadly Sin by Lawrence Sanders? I'd say that's a good reference for making a likable serial killer. You want to explore the strange logic with which the killer evaluates the world and his role in it. If done correctly, like in Sanders' novel, it makes a weird kind of sense. I liked the Affably Evil killer in that book the whole way through.

The key way to make the audience to empathize with a character is to show things from their perspective. How said character sees the world, with implications of the the character's past through subtle indication. Show the character's insecurities and fears, as well as how he was a product of his environment. A full blown psychopath like Hannibal Lecter is scary because of his alien morality, but it's impossible to sympathize since we can't relate with his situation. Provide an environment where we can understand how he became this way, as well as understand that he was a victim of circumstances. To sympathize with someone, we have to be capable of imagining what he has gone through. A child soldier is definitely sympathetic as we can recognize how horrible it is to send a child to war, we can imagine the brainwashing the child has to go through, we can feel anger for the child against the criminals who was willing to put a child through such atrocities as well as feel motivated to help them. Show moments of humanity and weakness so that it will be difficult for the audience to dehumanize him as another one-dimensional fictional villain.

Read The Shadow of the Tortuer by Gene Wolfe, Severian is what you're shooting for.