But it is religious to us Catholics. We choose life over death because in the New Covenant, mercy wins over justice. Our just punishment for sin is stayed because of the blood of Christ, the perfect propitiation for sinners.
Where your argument fails is in its wrongful attempt to assign immorality to capital punishment. You ask "What gives us the right?" and the quick, and devastatingly accurate response is God gives us that right. God instituted the death penalty as the backbone of human criminal justice in his covenant with Noah before mankind was once again spawned over the face of the earth and reinforced it with Moses when he gave the law on Mt. Sinai. This is what I learned, that when people who oppose capital punishment impugn those who support it as immoral, it repels them. And the reason it repels them is simple, it's not true. Capital punishment as a response to murder is not and is never wrong, and when we claim it is, we're written off as kooks.
The issue of capital punishment is not one of good vs evil, but rather one of a choice between justice, which is never wrong, and mercy, which is the better way. The Catholic Church offers a better alternative to execution, allowing somebody a lifetime to consider their actions and come to a state of repentance. Many murderers do arrive at this epiphany and are able to seek forgiveness. This is the better way.