Why the Night King didn't personally kill Jon Snow when he had opportunities:
1. He saw Jon as a greater threat alive than dead. The Night King repeatedly focused on his larger goal destroying humanity and the memory of the world represented by Bran Stark rather than pursuing personal revenge against Jon.
2. He preferred to let his armies do the work. Throughout the series, the Night King rarely fought directly. He relied on White Walkers, wights, and overwhelming numbers, as seen at the Battle of Winterfell.
3. Plot and storytelling reasons. From a narrative perspective, Jon was one of the central heroes. The story built him up as the leader against the dead, so having the Night King kill him before the climax would have undermined that arc.
4. The Night King underestimated his enemies. At Winterfell, he believed victory was certain and focused on reaching Bran. That confidence ultimately left him vulnerable to Arya Stark, who delivered the killing blow.
Ironically, despite years of buildup suggesting a final showdown between Jon Snow and the Night King, the series never gave them a direct duel. Jon's role was largely to unite the living against the dead, while Arya ended the threat.