How does Rikki-tikki’s decision to destroy Nagaina’s eggs contribute to the story?

Rikki-tikki's decision points the story toward its climatic battle between Rikki and Nagaina. Even though Nagaina's husband, Nag, has been killed, Rikki realizes that he must destroy her eggs to prevent more cobras in the garden. Darzee, a helpful bird, tells Rikki the location of Nagaina's eggs, then lures her away from them by pretending to have a crippled wing.
While Rikki-tikki is destroying the eggs, however, Nagaina stops chasing Darzee and instead corners Teddy to exact revenge for Teddy's father shooting Nag. Rikki saves one egg, then rushes over and taunts Nagaina, distracting her just long enough for Teddy's father to yank his son out of reach.
After saving Teddy's life, Rikki-tikki chases Nagaina into her hole, then emerges victorious a few minutes later. His heroic actions endear him to the family, whom he represents in the "man vs. nature" conflict against the snakes. His decision to destroy the eggs symbolized his devotion to Teddy, who had found him unconscious after a flood and nursed him back to health, and Teddy's family.
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Rikki-tikki's decision to destroy Nagaina's eggs is significant because he is able to get her attention while she stares down Teddy in the bungalow. Rikki-tikki wisely destroys twenty-four of Nagaina's twenty-five eggs and carries the last remaining egg with him into the bungalow, where Nagaina is focused on killing Teddy. Rikki-tikki is able to get Nagaina's attention by mentioning her eggs. As soon as Nagaina turns her head to look at her nest, Teddy's father grabs his son and pulls him to safety. Rikki-tikki holds onto Nagaina's last remaining egg as he begins dancing around her in circles. If Rikki-tikki had not destroyed twenty-four of Nagaina's twenty-five eggs, he would not have been able to get her attention while she prepared to strike Teddy. Rikki-tikki's decision to destroy Nagaina's eggs saves Teddy's life and allows Rikki-tikki to take the offensive in their conflict.