They're Made Out of Meat

In this science fiction story by Terry Bisson, two alien beings discuss their discovery that humans are sentient creatures made entirely of meat—including their brains. Despite initial disbelief, one character eventually convinces the other that these "thinking, conscious, loving, dreaming" meat beings have been attempting radio contact for nearly a century. The two aliens ultimately decide to ignore humanity's attempts at communication, reasoning that contact with meat-based life is too disturbing to pursue.