Sebastian Moore a Christian monk believes the origin of sin is not feeling good about ourselves. He believes that we are all born without sin but at some point the way we are treated makes us not feel good about ourselves. When we do not feel good about ourselves we do not act so well, so I would say the origin of hate is not feeling good about ourselves. The extent to which we move on or get stuck would depend on whether we have support around to heal us.
I do not believe hate itself is an emotion. I believe it is more an attitude. Anger is a totally normal and needed emotion for self defense. However hate has the objective of revenge. It is therfore not an emotion but an attitude coming from thought.
Psychopaths are not born this way. Psychopaths are incapable of empathy. This comes about because they have lost their ability to feel due to having been treated most cruelly. Psychopaths can be healed. A very gifted psychiatrist did this is a British prison. He worked with the most cruel psychopaths. He worked with them being the responsible parent they had never had and took them back through the most horrendous cruelty they had experienced. After this everyone, absolutely everyone noticed that these people began to have the one thing a psychopath can never have - warmth towards others and when you have warmth towards others you feel for others. When you feel for others you cannot harm them in the way psychopaths do so they were no longer psychopaths. (unfortunately this work was stopped throught lack of funding
)
Hating the behaviour is one thing but hating the person even if that person is a pedophile is in my opinion simply hate - justified hate maybe but hatred plain and simple. No different from other forms of hate.
We can choose to hate or we can choose to be there and heal each other - not to say that we are not all human and through our own life experiences may not feel hate at some time but in my opinion hatred of another human is always a failing and a failing in my opinion which is learned through our life's experience.
To continue to hold onto our hate when we realise it has been learned and can be changed is however a choice.
Hatred limits us and keeps us stuck. Forgivesness heals the person who forgives.
Edit: actually the choice or not choice is a difficult one. With the illustration of the psychopaths we can see that people often or indeed usually need their own pain healed to be able to let go of their hate. Possibly understanding can make a big difference but for a lot of people love and healing from others is also needed. However hate limits us and so is never a healthy attitude imo. Hatred of a behaviour or activity is fine because the way forward then is to work on healing and changing it but of the person it is never ok imo because then the attitude then is to want to harm the person.