why do you think voldemort didn't just kill snape with the old new avada kedavra, and why kill snape at all? he knew the elder wand didn't require the death of its previous master
I think that’s a really good question, because I’ve seen people theorize that Voldemort hesitated to kill Snape with a wand and used Nagini instead because he never actually intended, or wanted, to kill him. And while I do think it makes sense that he hadn’t initially planned to, the idea that he didn’t really want to can be answered differently. Voldemort was both frustrated and apprehensive that the Elder Wand did not recognize him as its true master. In fact, Voldemort had already convinced himself that the Elder Wand’s allegiance could only be secured through its master’s death. And for someone who consistently treats another person’s death as a sacrificial means to an end, Snape became the inevitable cost.
“Why doesn’t it work for me, Severus?”
In the silence Harry imagined he could hear the snake hissing slightly as it coiled and uncoiled — or was it Voldemort’s sibilant sigh lingering on the air?
“My — my Lord?” said Snape blankly. “I do not understand. You — you have performed extraordinary magic with that wand.”
“No,” said Voldemort. “I have performed my usual magic. I am extraordinary, but this wand . . . no. It has not revealed the wonders it has promised. I feel no difference between this wand and the one I procured from Ollivander all those years ago.”
Voldemort’s tone was musing, calm, but Harry’s scar had begun to throb and pulse: Pain was building in his forehead, and he could feel that controlled sense of fury building inside Voldemort.
Being caught between a furious Dark Lord and the very object he believed would most legitimize his claim to power — a tool that was refusing to answer to him — left Snape, one of his finest Death Eaters, as the sacrifice Voldemort believed had to be made in order for the Elder Wand to finally acknowledge him. In Voldemort’s eyes, anyone in Snape’s position would have met the same fate simply by standing, however indirectly, in the way of Voldemort’s legitimacy as the wand’s “true master”.
“The Elder Wand cannot serve me properly, Severus, because I am not its true master. The Elder Wand belongs to the wizard who killed its last owner. You killed Albus Dumbledore. While you live, Severus, the Elder Wand cannot truly be mine.”
Besides Voldemort already being bothered and uneasy that the wand wasn’t working, it also perfectly explains why he wouldn’t have wanted to risk his own Killing Curse rebounding and killing him instead (he has experienced this before). So why take that risk by casting the spell directly at the wizard he believed to be the Elder Wand’s master, when he could already feel the wand resisting him? Using Nagini was the next most straightforward solution.
Moreover, unlike the final duel between Harry and Voldemort — where Nagini was no longer an option, forcing Voldemort to rely on Avada Kedavra (his most powerful spell) in a far more critical and emotionally charged moment (when he was visibly desperate) — here, as Voldemort himself says, he could stil find himself “wondering, wondering, why the Elder Wand refuses to be what it ought to be.”
There was a terrible scream. Harry saw Snape’s face losing the little color it had left; it whitened as his black eyes widened, as the snake’s fangs pierced his neck, as he failed to push the enchanted cage off himself, as his knees gave way and he fell to the floor.
“I regret it,” said Voldemort coldly.
He turned away; there was no sadness in him, no remorse.
Also, I think it’s significant that the narrative deliberately uses two closely related words when describing Voldemort’s emotions. I’ve seen people conflate the two, since both are associated with sorrow depending on the context. But here, Voldemort’s regret comes from disappointment; from believing the situation could have unfolded differently and spared him the necessity of Snape’s death, a death he relied upon because of the decision he believed he had to make.
In other words, he regretted the outcome, but he did not repent of the decision itself. To Voldemort, Snape was the necessary sacrifice. So he didn’t kill him simply for the sake of killing him. At the same time, he felt no remorse after Snape’s death.
Even though Voldemort regarded Snape as one of his best Death Eaters, Snape was still a Death Eater. And like every other Death Eater, he was ultimately a pawn beneath the Dark Lord; someone expected to take risks and, if Voldemort deemed it necessary, to die for the outcome of those risks.