Psychopathy simply means "mental disease" - 'psych' = mind, 'pathy' = illness. Its probably a spectrum, and probably everyone is a little bit messed up in the head. I do think that stronger meaning of the word applies to people who advocate the death penalty. Maybe some people simply haven't thought it through, but I don't think most people fall into that category.

I do agree with you that people have a right to revenge, but this is the only instance I can think of that a right should be denied. Justice is supposed to work better than revenge, so we should ensure that our justice system is actually delivering justice. I live in the US, and I would emphatically argue that there is no justice in our court system, for many reasons.

There are three main problems with the death penalty. 

First, as someone already wrote, if an individual doesn't have the right to kill, for any reason, then a group cannot magically have the right to kill by virtue of being a group or having some higher status. 

Second, no human is perfect. If no individual is perfect, then no group is perfect. Their judgement may be wrong. Evidence and testimony may be faked. Incentives may reward them for judging wrongly. Power structures may be threatened, and the politics may demand the death of an innocent. None of these possibilities can be ruled out.

Third, similar to how the judge and jury are imperfect and subject to incentives, the same is true of someone who actually did kill. Even if you know absolutely that they did it, its still wrong to kill them. Incentive structures are generally out of our control, and they work in positive and negative ways, and they work in both the short and long term. For example, the current monetary system of usury and perpetually devaluing money causes some amount of stress in people. How much stress? Impossible to know. It affects different people differently, and social emergent phenomena could amplify stress more on particular people, and those people will be more likely to break and do something violent. Entire belief structures are built around compensating for felt oppression. For example, both the state and religion are belief structures that relieve people's anxiety - these social structures emerge from fear. And both the state and religion cause people to kill, and they will never define such killing as murder. But would these structures even exist without the constant application of stress on people, subconsciously felt, from the devaluing of people's savings and work? You can see that, at least partially, incentive structures are self perpetuating cycles. The things that motivate behavior are mostly subconscious and out of an individual's control. Its not simply, "he decided to kill, he's just bad." That doesn't exist. That's a fantasy. And if justice boils down to such a simplistic view on behavior, then there's no hope of ever having 'justice.'

This is too long already. I'll reiterate that the death penalty is wrong, and say that there are other options. And I'll reiterate that someone who thinks society should repay murder with murder is a psychopath. Definitely.