Looking for this story for a while. Probably from an anthology. Read this many years ago. Earth is under attack by creatures that I recall are on a non-physical plane. Sentient cat brains are wired into the fighter ships to meld with the human co-pilot, taking advantage of the cat's superior nervous system and predator instincts. The bad guys appear to be rat-like - or made to look like that by the ship's software to entice the cat fighter to engage. A fun concept, but the real story is a love story: The human protagonist is falling in love with his feline fighting partner. As I recall, he is married, and his wife is becoming more suspicious. I loved how it described the cat's fighting instincts and why the man loves her.
I suspect you are talking about The Game of Rat and Dragon, by Paul Linebarger (aka Cordwainer Smith.)
Do the names Underhill, Lady May, Woodley, Father Moontree, or West ring any bells?
From the Wikipedia article: "Cats guided by telepaths are used to fight the "dragons", because of their very quick reactions. They see the aliens as giant rats, hence the story title."
Re: the romantic side: "Underhill is hospitalized and a doctor tells him that he was within a tenth of a millisecond of going insane, but the only thing that concerns Underhill is his partner, Lady May, and her well-being. A secretly jealous and angry nurse walks in and Underhill compares her to Lady May. Logically, he understands that Lady May is only a cat, but his mind tells him that no woman will ever equal her."