Continuity mistake: When Klaue is being rescued by Erik, the amount of blood from his face wound changes between shots.
Continuity mistake: Towards the end of the film: Killmonger is about to kill Shuri at the top of the mine shaft and Shuri is backing up. Her elbow goes over the edge, but in the next shot which is from over Killmonger's shoulder looking down at her, she is at least a foot away from the edge.
Continuity mistake: When M'Baku challenges T'Challa, the decorations near his neck are in a different position between him facing the crowd, and him turning to face T'Challa.
Continuity mistake: When Ross is interrogating Klaue, there's a shot from behind him and we can see the bug on his left shoulder. When he leaves the room and talks to T'Challa, the bug has vanished, but reappears again shortly afterwards.
Continuity mistake: While T'Challa is fighting in his first challenge, the sun changes between shots.
Continuity mistake: When Killmonger cuts a woman's throat, in one shot a spear is not red, but in the very next shot it is.
Answer: Zuri feels guilty for his role in the death of Killmonger's father, which is why he tells Killmonger to kill him instead of T'Challa. While Zuri himself probably doesn't actually want to die, I don't think he wants Killmonger dead either, which is why he wouldn't kill him. Also, as a royal advisor, it would probably be looked down upon by the other tribes if he violated the rules of the ritual combat. After all, one combatant has to defeat the other in order to rightfully claim the throne.
Phaneron ★
Zuri may not want Killmonger to die, but he knew that the duel would only end once one of the contestants would either surrender or die, meaning Killmonger would stil win or kill T'Challa. It seems a rather low price to be looked down upon or fired if it means your country doesn't go to war. At least, that would be a small price to pay for keeping the peace.