“My pod’s defective”

TAYLOR: You have lived in Stars Hollow for a long time, young man. It’s time you became one of us.
…
LUKE: Sorry, I guess my pod’s defective.

A reference to the 1956 sci-fi horror film Invasion of the Body Snatchers, directed by Don Siegel and based on the novel The Body Snatchers by Jack Finney. In the film, residents of a Californian town discover that they are being replaced with exact duplicates of themselves, grown from giant seed pods as part of an alien invasion. The duplicates are devoid of emotion and have no sense of individuality. Ignored by critics on its release, this 1950s political allegory is now considered a classic sci-fi film.

The fact that both Lorelai and Luke use 1950s sci-fi films as a reference in their conversation is a sign of their compatibility. We earlier saw Luke is concerned for the environment, and the environmental message of Invasion of the Body Snatchers, as the pod people are there to use up resources and destroy ecosystems, may have appealed to him.