Fact from fiction, truth from diction. Looking from it from a purely secular lean as the OP requested, when it comes to serial killers I don’t think there are reasons why they kill, not that any of those reasons excuse the killing but they maybe valid to why they kill.
A. The serial killer is very narcissistic; they want to hold power over people by terror they feel they cannot get any other way. In some fearful way people respect them because of what they can do and have done even if the people do not know who they are.
B. They devalue life, no one is important. Just about everyone else to them are no more important than cockroaches.
C. They had little or no checks or brakes to quash those malevolent feelings when they were children growing up. Be it they had hands-off parenting that left them pretty much to their own devices and cravings that once adult, or near so, they could see no harm in their actions.
D. Severe anger issues, they felt live have treated them so badly that they want to extract some form of vengeance to counter their hurt. Whether or not they believe a certain class of people, a certain race or people, women, society in general or the government is the reason for their failures, I can’t say.
E. They have a mental abnormally, some chemical missing in the brain causing their neurons to misfire, or hampered their reasoning. Then again, leave it to some arguments, that is how they were suppose to be that being off emotionally, or unable to control their cravings is normal for them; seeing normal is suppose to be subjective.
It could be any of those, or a complete mystery; maybe something mankind has yet to even grasp yet.
Personally I see serial killers no different from professional torturers, redacted, redacted, and redacted.