I've been having a search for this, and apparently the answer is TAUTONYMS, which are words or terms made from two identical parts or syllables.
The teacher hates me... because tautonyms are no longer allowed in botany
Cow likes me... Bison bison is tautonym for American Bison
Monkey eats me...Ziziphus zizyphus is tautonym for jujube, a fruit-flavored, usually chewy candy or lozenge, liked by monkeys.
My first thought was nuts. Teachers hate nuts (as in foolish people) cows like cattle nuts (type of feed) and monkeys eat monkey nuts, but hell, what do I know?