2. Jesus overturned the Old Testament law that allowed retributive violence.
I remember learning about the death penalty as a child and the first thing I was taught was that the Bible says “an eye for an eye”. This principle of an eye for an eye (something that many scholars believe at the time was designed to reduce violence by limiting it to a proportional response) is called the “Lex Talionis”. What I find most peculiar with this argument, was that I was never taught that Jesus very explicitly went on the record in telling his followers to no longer obey the Lex Talionis:
38 “You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ 39 But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also. 40 And if anyone wants to sue you and take your shirt, hand over your coat as well. 41 If anyone forces you to go one mile, go with them two miles. 42 Give to the one who asks you, and do not turn away from the one who wants to borrow from you.” Matthew 5:38-42
So yes, it is true the Old Testament allowed capital punishment and retributive violence. Jesus however, weighed in as disagreeing with this principle- or at a minimum, instructing that it should no longer be observed. Therefore, it is not possible to argue a Christian case in support of the death penalty while citing passages from the Hebrew scriptures, because this will put one at odds with Jesus himself.