This article mentions the dollars and cents expense of the death penalty; this is an empirical fact, either it is cheaper to execute someone or cheaper to imprison them.
This article mentions the ineffectiveness in protecting society; this is also an empirical question, although it is harder to measure than the monetary cost.
Finally, the article speaks of the emotional and moral cost to those employed to carry out the execution.
But the article only devotes a single sentence to the core of the argument, at the very beginning: the author has come to believe that life is either hallowed or not, and he prefers to believe that it is always hallow, and killing always wrong.
This is the core of the problem. Some people believe killing is always wrong. Some people believe justice requires the execution of those convicted of a capital crime. Heck, sometimes these contradictory beliefs are held by the same person.
All the other arguments don't matter. If killing is always wrong, you pay the cost of life imprisonment and don't execute people to save money. If justice requires a life for a life, you don't scrimp on that, either. You pay whatever monetary, emotional, and moral costs are necessary for justice to be done.