Because its the only power we have to live in a world we truly wish to live in. To hold that belief and enforce it in your daily life is the only way to make it real. That we are not intelligent enough to really truly judge something objectively, so we should err on the side of compassion. Because you never know when its going to be your head on the chopping block.
'A world we truly wish to live in' is a pretty vague goal-- do you really think that humanity has a single universal vision of their ideal world? Don't you think that if this were the case, and everyone agreed that caring for each other made everything better, then we would have already solved all of our 'problems'? You don't think it's possible that we'll never be truly happy with anything? Or that the only happiness/peace that people could ever achieve involves contenting ourselves with the world around us on an personal level?
In the grand cosmic scheme of the universe, it's likely that we're all insignificant and so it really doesn't matter what we do or how we feel about anything... but on a human level, we DO have an interest in being cold/not showing compassion/caring to certain others... namely, the destructive influences. And by that I mean the people who intentionally, unapologetically commit hugely destructive acts only for their own pleasure.
If it were my head on the chopping block, then how deserving of sympathy I would be would probably depend on the reason I'm there. There's a difference between the people who don't think that unwed mothers should get welfare (that's just cold/ignorant/selfish) and the people who think that serial child molesting murderers should be given the death penalty (that's a little more reasonable).
If we were living in a society where people were actually in demand, then I would probably advocate greater compassion but we don't actually NEED hugely destructive forces in our society and accommodating them/showing sympathy for them seems counterproductive.
I guess there's always the potential that they might 'see the light' one day, but at best they're going to be unexceptional... another waste of space in a world where space is disappearing rapidly.Why would we waste time and effort trying to get them to the point where maybe they can edge out a good person to become the bagboy at your local supermarket?
They'll be forgiven when they're forgotten. Death is extremely compassionate-- it treats everyone equally.