Why is the cathode of a lithium-ion battery metallic, which is the opposite of most other batteries?
This is not entirely true.  Wikipedia lists several possible cathode materials and they are oxides.  They may be &quot;metallic&quot; is the sense of being metallic conductors (some oxides are so), but they are ceramic compounds.
In secondary batteries the anode is typically Li-intercalated carbon (which is also a good conductor).  Lithium intercalates readily into carbon, allowing a safer and less side-reaction prone choice than pure lithium, whereas most other metals do not.