Well, this part of the Potterverse gets really deep. Voldemort's killing of Snape was a matter of convoluted intricacies, rooted in his beliefs about the Elder Wand's allegiance. Voldemort believed in the 'wand ownership transfer through murder' theory. He was convinced that Snape, who had killed Albus Dumbledore, was the master of the Elder Wand.
Consequently, he believed that to become the rightful owner and unlock the full power of the Elder Wand, he needed to kill Snape. Now here's where it gets darkly ironic. Voldemort, an epitome of cunning and power, was misled by his own theories. The Elder Wand's allegiance had already shifted to Harry, not through murder, but disarmament. Draco Malfoy, not Snape, was the one who'd disarmed Dumbledore prior to his death. Harry later disarmed Draco, making him unbeknownst the wand's genuine master.
Yet, Voldemort's misinterpretation led to Snape's tragic end. Snape dies, in the end, revealing another truth to Harry through his memories—a truth about his undying love for Lily Potter. Snape's death, thus, turned out to be one of the most heartbreaking moments in the books. Through his death, a misunderstood character transformed into a tragic anti-hero, etching a permanent place in readers' hearts.