It’s odd to me how controversial both issues are when the moral reasoning required is so easy. Taking any other position requires denying the premise that it’s wrong to destroy innocent human life. One can, but accepting that has some very nasty consequences.
Death penalty is any easy one. It was considered to be a proper penalty for various crimes for most of the human history in many cultures. It just takes understanding of ethical values of those cultures to understand why it was justified.
Your argument about taking innocent human life is a naive one. We do a lot of things that cost innocent human lives. Allowing diesel cars in cities cost more innocent lives than all death penalties in the history of humanity combined and it's not a small difference.
It's about tradeoffs and priorities. It's natural for a tribe or state to kill for treason for example as disincentivizing treason is more important (saves more lives, prevents suffering and destruction of your countrymen) than occasional mistake. Putting long term survival and well being of your society is more important than individual lives.
Our wealth clouds the picture so well. If it was required of everyone one to spend addition 20 hours a week providing food and shelter for a murderer atop of all the work we need to put into getting food and shelter for ourselves and our families you would be very quick to accept death penalty instead. As the choices would be about caring for your family and making sure the murderer doesn't die in custody. Today we can arguably afford it but if that's the argument then we already agree it's about tradeoffs and where the exact line is not obvious.
Even if you don't agree you can at least see it's a justified view. It's all about tradeoffs.
If we just use this argument and don't try to establish general principles we end up with a pointless shouting contest.
For once I think the death penalty is at least worth considering from the utilitarian point of view (in our current system the consensus is that it's cheaper to keep someone in prison for life though but it might change in the future) as well as from revenge/restitution point of view as a lot of people strongly think someone doing deliberate great harm deserves to be killed.
One way or another it's not simple from either ethical nor practical point of view. Personally I consider death penalty as desirable penalty for some crimes but I would never vote for it as I have no faith in our politicians being able to implement it in a fair way and flawed justice system not to abuse it.