they eats eggs!
he was anxious to learn where did nagaina had hidden her eggs because he wanted to eat them .
darzze the bird's wife distracted nagaina
he was going to kill her and her eggs
Rikki-tikki is anxious to find where Nagaina has hidden her eggs because he knows that if he doesn't destroy them, they will hatch into dangerous cobras that could pose a threat to the family he is protecting. He understands the importance of eliminating the eggs to ensure the safety of the family.
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Rikki kills Nagaina by tricking her into chasing him into a hole where he confronts and kills her eggs. Nagaina then comes back to attack Rikki, but Rikki kills her by biting her in the neck.
First of all there are eggs with Nagaina that will help her in killing Rikki. Second because Rikki killed her husband so she might be stricked and do many plans to kill Rikki.
Rikki fought Nagaina to protect the human family and their egg from harm. His primary motive was to ensure the safety of the bungalow and its inhabitants, which included hunting down Nagaina to prevent her from causing further harm or laying eggs that could threaten the family.
Rikki-Tikki' wants to destroy Nagaina's eggs contributes to the story by driving the action forward towards the main conflict and ensuring that there will be no more cobras in the garden, at least in the immediate future. The destruction of the eggs leads to the final conflict between Rikki-Tikki and Nagaina.
If they hatched there would be even more snakes to deal with.
so he can eat them