We shouldn't necessarily feel sympathetic towards murderers, because sympathy means that you share in their feelings/pain. We don't share their pain, and in most cases, we don't understand their psychology. However, we should feel empathetic towards murderers. We should pity them for allowing their situation to play out like it did.
Murderers must have had some kind of horrible background or must have had something horrible happen to them as children. They must have completely destroyed mindsets and must be completely lost. They are human too. We can't be so cold as to completely cast them into darkness and horror--they should be punished of course, but we should feel sorry for them--it's part of human nature.
Only in this one point do they deserve any sympathy or compassion, that somehow they missed the boat in understanding the gravity of this offence. They are incapable of fully functioning in human society and must be removed from it whether by capital punishment or incarceration. The question of how they became that way or what motivated them to kill can justify empathy for them because however it happened they were a cog in the wheel and seemingly unable to change it within themselves. Somehow they missed out on whatever human considerations make murder so wrong to the rest of us.
Murder is the worst crime someone can commit. To murder is not a planned response; it is usually a spur-of-the-moment action. The person who murders, is usually from a poor background, and has had society against them from birth. They have been conditioned by society to answer disagreements with violence. When a middle-class person would walk away from an argument or escalate to a screaming match, a lower-income person would be much more likely to respond with violence, up to and including murder.
In order to commit murder, someone's mind has to be broken beyond repair. While this does not excuse their actions, I do think they deserve sympathy for their illness. We can punish them for their crimes, and still feel compassion for them, and how very sick they must be to commit such a terrible crime.
Most murderers choose to murder. They choose. Before you say "Oh. But they have mental conditions!" Then why didn't they call for help? I know some can't and those are the ones I care about. But most murderers murder for the sake of seeing someone die. Doesn't it sound twisted? Being poor isn't an excuse. Because most of the poor people I've met were kind. Also not knowing the law isn't an excuse either. I see the law everywhere I go. Being young is still not an excuse. When you were all young weren't you taught that killing someone was mean, gross and wrong? Kids weren't taught to murder. Sorry if I sounded mean, I was just trying to get my point across.
There may be extenuating circumstances, cases where I would feel sorry for the murderer. The battered wife who kills her abusive husband for example. But generally, no. Murder is above anything else, WRONG, just WRONG. Being from a poor background is not an excuse. Even poor communities teach their children that "murder" is wrong. There may be more factors at work that may encourage a person to resort to murder, but in the end it is still that person's choice and that person still knows what they are doing is wrong. Furthermore, beyond what society teaches I think there's something in our very nature that says "THIS IS WRONG!" Even if that were absent, then it can be taught and with very rare exceptions (like being raised by someone apart from society and indoctrinated) it is whether by parents, in a school civics classroom, or in a church, synagogue, mosque.
One of the worst things you can do is kill another person. It is cruel, inconsiderate, and just a downright terrible thing to do. Anyone that murders does not deserve to have any type of sympathy. Why should someone feel sorry for a killer? The killer did not feel sorry for those they murdered.