First, I want to thank you for your reply which contains many scriptural references.
I would think it would be the responsibility of those who disagree with the Pope and with the teachings of their own (Catholic) church to provide the evidence against the Pope, the teachings, and Jesus.
That's kind of the topic of the thread, isn't it? What we're talking about is whether the Pope's decision was a good one in light of Church teaching, tradition, and scripture. I'm not arguing against the Church or against Jesus, I am arguing against you. To claim, right off the bat, that I am at odds with the Church or Jesus is a fallacy called 'begging the question.'
Jesus clearly condemns killing (which in most of our minds would include capital punishment) and in fact goes so far as to say that being angry with our brother violates that commandment.
Good. "That commandment." Jesus' teaching on killing always hearkens back to the decalogue, to what Catholics number as the 5th commandment, "Thou shall not kill."
There are very few Catholic, Jewish, or Protestant Biblical scholars who believe the 5th commandment prohibited capital punishment. Indeed the Old Testament law explicitly includes and commands capital punishment (cf. murder: Exodus 21:12-14; Leviticus 24:17, 21; Genesis 9:6). There is no reason to believe that Jesus, a faithful Jew, disagreed with the entire Jewish tradition up to that point with respect to the 5th commandment.
I dislike "Chapter and Verse" arguments but I will list some places where you will find Jesus's teaching...
While I appreciate the effort, simply throwing out allusions to a half-dozen
chapters of the New Testament just isn't conducive to dialogue, nor does it constitute a very strong argument. Beyond that, the principle that I gave above addresses each of your examples. Like a good Jewish teacher, Jesus is highlighting and reiterating things found in the Torah and other parts of the Hebrew Bible. As with the 5th commandment, there is no reason to believe that these teachings from the Torah contradict the Torah (with respect to capital punishment). At the very least, the burden of proof is on you to demonstrate such a strange fact. If you want to give a more specific example you are more than welcome. I will address "the best example":
I will list some places where you will find Jesus's teaching about this and about the necessity to follow ALL of the commandments, and of the necessity to love our neighbor if we want to attain God's Kingdom: Matthew 5 (this is really the best example, as Jesus spends a lot of time in the Sermon emphasizing this--sorry, no way to get around it),...
Okay, Matthew 5. Since you mentioned "the necessity to love our neighbor," I assume you are talking about verses 43-48 where Jesus speaks of love of enemies.
In Matthew 5:43 Jesus is quoting Leviticus 19:18 where the Hebrews are instructed to "love your neighbor as yourself." He is saying that this love should be extended even to enemies, even to those persecutors who are despised. This does not mean that the state does not have the power to execute criminals who are guilty of capital crimes. The grounds for execution are not bearing a grudge or despising someone, but rather redressing the disorder caused by the offense and satisfying justice. The OT does not say to execute on the basis of anger or a grudge, it says to execute on the basis of a transgression of God's law, such as murder. No one thinks we need to kill people in order to satisfy a grudge and get revenge. That's a classic strawman.
If you think that the passage from Romans says we should disobey Jesus, the Gospels, and God's commandments (and that Paul takes precedence over Jesus Christ), then you have a problem. Reading that writing carefully, you will see that Paul implies that all those in authority are good and should be obeyed. We know that is simply not true.
You're begging the question again. You're committing a fallacy. I don't think Paul contradicts Jesus, the Gospels, or God's commandments. I don't think Jesus, the Gospel, or God's commandments prohibit the death penalty. That's what we're arguing about,
remember? 
But Paul is pretty clear. I've actually researched this question and the vast majority of Biblical scholars are in agreement that by "the sword" Paul is referring to civil leaders' power to execute criminals in capital cases. Even you seem to agree that this is what Paul is talking about, for you certainly didn't object (you just told us Paul was wrong).
So maybe you are the one who thinks Paul contradicts Jesus, the Gospels, and God's commandments? Maybe you are the one who needs to pick and choose who takes precedence: Paul or Jesus? In that case, yes, "You have a problem." Because the Catholic Church teaches that
all scripture is inspired. You don't get to just throw away Paul's words about capital punishment--
the only words that explicitly deal with capital punishment in the entire New Testament! 
It is not rocket science.
It's not rocket science, no. In fact our Church has been studying and defending the scriptures for 2,000 years. It would be a pretty big oversight to miss that part of the Bible that so obviously prohibits capital punishment.
Honestly, this whole effort is somewhat silly. No Catholic theologian thinks this question can be easily settled on the basis of scripture. That's naive. It certainly can't be settled in the direction of a prohibition! John Paul II never quoted scripture as a direct support for his position on the death penalty, and I don't believe Francis has either.
It looks like your vague claims about Jesus and the gospels haven't come through for you. Maybe all those people who disagree with you are Christian after all? Maybe they are civilized and clear-thinking, too?
Best,
-Zip
