Firstly, no one really believes that they are evil. "Crazy people don't think they're crazy" and people who think they're going crazy are not, or at least they find a sane reason for the stress causing them to feel this way.
No one believes that they are really evil at heart. Insane people will have reasons for the way they behave and in their own reality these reasons are completely valid, if not essential, to feed their needs and passions.
Serial Killers in their own minds are the heroes of their own stories. They believe what they are doing is right and must be done.
The antagonist of the story is the Serial Killer AND the person who we think is the serial killer.
We will see many links in the nature of both father and son. In their movements and actions, without ever seeing the son.
Serial killers may be able to convince themselves and others that they 'understand' why we 'feel' their actions are unacceptable in society, but they do not agree with us.
There is always a power struggle in everyones mind between right and wrong. There must be a balance in the serial killers trend. Not all murders can be disgusting or vile, some can be similar in nature but not all shocking. This would make it too OTT.
There must be a balance that reflects a human element to the serial killer not just a feral insane person.
What motivates them to do what they do? What allows them to believe that what they are doing is normal? Do they realise that it is not normal - they are in hiding after all? Surely, they know that they are not normal. What effect does this have on them?