why macavity is a mystery cat ?

the reason is

The poem Macavity the Mystery Cat is the best known of Eliot's Old Possum's Book of Practical Cats, the only book Eliot wrote for a younger audience.[1] The poem is considered particularly suitable reading for 11 and 12 year olds.[2]

Macavity (also called the Mystery Cat, the Hidden Paw and Napoleon of Crime) is a master criminal, but in the poem he is too clever to leave any evidence of his guilt. There is a resemblance with Professor James Moriarty from the Sherlock Holmes stories by Arthur Conan Doyle. In a letter to Frank Morley, Eliot wrote, "I have done a new cat modeled on the late Professor Moriarty, but he doesn't seem very popular; too sophisticated perhaps."[3] Sherlock Holmes describes Moriarty as "the Napoleon of Crime" in The Adventure of the Final Problem and a "Napoleon gone wrong" in The Valley of Fear. The idea that Macavity was Moriarty was first revealed by HT Webster and HW Starr (Macavity: An Attempt to Unravel His Mystery, 1954), an identification rediscovered by Katharine Loesch.[4]

According to the poem, even when the Secret Service decides that Macavity was behind a loss, they can't get him there as "he's a mile away." Doyle wrote that Moriarty "is never caught" as at moment of crime he probably is "working out problems on a blackboard ten miles away" (The Adventure of the Final Problem). Macavity is described as being a ginger cat who is very tall and thin with sunken eyes, and "sways his head from side to side with movements like a snake". The poem also says: "His brow is deeply lined in thought, his head is highly domed; His coat is dusty from neglect, his whiskers are uncombed." Once again, this description is a close parallel to that of Professor Moriarty:

"His appearance was quite familiar to me. He is extremely tall and thin, his forehead domes out in a white curve, and his two eyes are deeply sunken in his head...his face protrudes forward and is forever oscillating from side to side in a curiously reptilian fashion." (The Adventure of the Final Problem)

The poem accuses Macavity of misbehaviour that would be within the capabilities of an ordinary cat, such as stealing milk, but also holds him responsible for major crimes. He is referred to as a "fiend in feline shape, a monster of depravity" and has been suspected of stifling Pekes, vandalism, theft, cheating at cards, espionage and controlling an organized crime ring with Mungojerrie, Rumpleteazer and Griddlebone among the members. Holmes in Doyle's narrative describes Moriarty as "the organizer of half that is evil and of nearly all that is undetected in this great city."

Webster and Starr assumed that Eliot referred to the cases of Mr. Joseph Harrison (The Adventure of the Naval Treaty) and Herr Hugo Oberstein (The Adventure of the Bruce-Partington Plans) when he wrote in the poem "And when the Foreign Office finds a Treaty's gone astray,/ And the admirality loses some plans and drawings by the way".[5]

Macavity apparently possesses the mystical power of levitation, as he "breaks the law of gravity"