"Only the state shall kill" Scanners live in vain, by Cordwainer Smith.
Here I will present a few brief arguments against the capital punishment.
Argument #1: Not a deterrent.
There is no correlation whatsoever that the death penalty makes people less likely to commit capital crimes. In fact, areas of the United States that do not institute capital punishment actually have a lower crime rate. 
Argument #2: More valuable alive than dead.
While putting a criminal to death provides the visible payment of a feeling of justice the surviving aggrieved, there is also the invisible cost of the loss of the potential service that the death row inmate can provide for society as a living example of the consequences of aberrant behavior. Furthermore, it costs more to kill that to let them live because of endless court appeals.
Argument #3: Racism.
By the numbers: prosecution 20% more likely to seek death penalty if the victim was white, and blacks receive are executed at a 38% higher rate than whites. 40% of people believe that they would be disqualified to serve on a jury determining guilt in a capital punishment case because of their race.
Argument #4: Gender.
Only 2.9% of all executions in the United States have been women since 1602; only 13 women executed since 1976. The fact is that juries are far less likely to sentence a woman to death even if under the law they should have.
Argument #5: Innocence.
To date, 142 people have been found innocent after having been sentenced to death. 14 of these have been because of advances in DNA procedures. What new technology might be used in the future to exonerate the false imprisoned?
If there is to be a death penalty it must be applied impartially and we have failed to do so. Criminals almost never use foresight in considering their capital crimes. In killing these people we fail to put them to work educating society in a positive manner. Let these people be seen and heard. That might be true deterrence, true repayment, true vindication if they are proven innocent.