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Although these organisms appear to be very different, plenty of evidence suggests that the lobster and the cockroach are more similar than many people might think! They are both arthropods with segmented bodies, exoskeletons made of chitin, and a need to molt as they grow. Both groups have compound eyes, jointed legs, and muscle fibers gathered into bands. (Is that why they taste good?) On a more superficial level, lobsters and cockroaches are both active at night and omnivorous, consuming a wide variety of foods. And while the arthropod phylum contains lots of other creatures, such spiders and centipedes, anatomical and DNA evidence all support the idea that insects and crustaceans are more closely related to one another than to the other arthropods.
I realized this once while eating one, but to my surprise I was not nauseated. Quite the opposite. I had been enjoying the lobster so much that I wondered how cockroaches taste.
Green crabs are perfectly good to eat -if, and only if- they are caught in a non contaminated area.