Can you teach your cat to fetch? Maybe.  But I got a cat that teaches me how to throw.  Then demands it.   
She brings some toy to me as I lay on bed watching the tube. 
She says”. Throw it , dummy”. In Ragdoll ( that’s what kinda cat she is). 
I, obediently, throw it.  She brings it back. And says, “. I said Throw it, schmuck.”   I think she’s Jewish. 
I throw it again.  This time she dips the toy in her water and brings it back, wet, and drops it on my bare chest.  “ Sheeit”. It’s cold and wet.  I throw it again, angrily and wet. She says, “ Screw it.  If you’re gonna get mad , I don’t wanna play anymore”. And she jumps off the bed. Game over.  Dogs have masters. Cats have staff.