Would you rather be put to death quickly, or slowly rot in some forgotten cell. Years and decades passing you by. The same four walls staring at you every single day until you breath you last.
Also keep in mind the difference between all sorts of ways to kill people. You have premeditated murder, murder due to acts of passion and anger, killing someone after drunk driving, medical negligence, being a lazy inspector on buildings, airplanes, ships, etc.
I can support the death penalty for mass shooters or serial killers, but the death penalty has to require a lot of oversight. Otherwise we end up like China and using political dissenters as spare organs.

It's interesting that you see an asymmetry between how certain American institutions deal with violent dogs and violent humans and automatically assume that we're responding appropriately in one place vs the other.

Someone could just as easily make the statement that if we're going to extend compassion to convicted humans who know beforehand the consequences involved with violence, it follows that we ought not kill violent dogs, who weren't (and couldn't be) sufficiently informed beforehand of the downstream effects of such violence.

The death penalty represents a certain idea of power that the state has over someone's mortality. The problem is if the state can control that mortality over a criminal that the mob argued in, then the said mob will have enough power to trust the state even more, and more, and more until the government become potentially tyrannical. It is not too far of a stretch but then again there have been countries where ultimate dogmatic governments do not spawn from this that have this capital punishment. I need to research more on this manner though for a clear and precise debate though.

I'd also like to point out that we regularly take human lives just for being conceived.

While I'm not against the death penalty per se, all the same I don't think the states deserve to have that kind of power.

One major difference in the two scenarios, a person bitten by a dog can identify the exact dog that did it. In a murder case there is room for error unless u have video or DNC proof of 100% accuracy. I'm not against the death penalty but I think it should take a very strict level of proof in order to be administered. As far as the cost go, I have seen things that way it's cheaper to keep them alive than it is to execute them. I don't see how that really works out but I've seen it reported and claimed tho.