Sorry for taking so long to get back to this.
Vengeance for murder is mandated to Noah, as the leader of all mankind, in Gen 9:5-6:
And surely your blood of your lives will I require; at the hand of every beast will I require it, and at the hand of man; at the hand of every man's brother will I require the life of man. [Gen 9:5 KJV]
Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man. [Gen 9:6 KJV]
The bolded part in particular specifies that it is man that must avenge murder (v.6).
And is reiterated in Num 35:19, 21.
The avenger of blood himself shall put the murderer to death; when he meets him, he shall put him to death. [Num 35:19 NKJV]
or in enmity he strikes him with his hand so that he dies, the one who struck [him] shall surely be put to death. He [is] a murderer. The avenger of blood shall put the murderer to death when he meets him. [Num 35:21 NKJV]
So, if Moses in Numbers 35:19
affirms the concept of the avenger of blood, why would he then
disavow the concept in [Deu 32:35 NKJV]: 'Vengeance is Mine...', which Paul quotes in Rom 12:19?
So either God changed His mind between Numbers and Deuteronomy, or Paul is pulling the verse out of context for a new purpose, or there's something else that doesn't make sense with what you are saying (that murder is never to be avenged by humans). The jurisdictional thing is the best answer I have to keep the texts consistent with each other. Num 35 goes into some specific detail about how the murder trials are supposed to work in concert with the "sanctuary cities", and seems to indicate that 1. the avenger of blood is not to also decide guilt (separating judge from executioner), and 2. multiple witnesses are required.
Just thinking through the "personal" vengeance idea--with respect to murder, there is no "personal" vengeance, since the victim can't take vengeance. Deut 32:35 seems to be concerned with "national" vengeance, and Paul co-opts it for a more personal use, in all cases where "personal vengenance" would apply (which does not include murder), showing a side of Christians that should set them apart from most others.
Sidenote: