In the question How did Ginny Weasley set the Basilisk on Muggleborns without getting killed or petrified?, Tom Riddle mentions that he had Ginny set the Basilisk on Mrs. Norris, Filch's cat.
‘Ginny Weasley opened the Chamber of Secrets. She strangled the school roosters and daubed threatening messages on the walls. She set the serpent of Slytherin on four Mudbloods, and the Squib’s cat.’
Chamber of Secrets - page 229 - Bloomsbury - chapter 17, The Heir of Slytherin
Why would Riddle want Mrs. Norris to be petrified? Mrs. Norris is definitely a snoop and a tattletale, but there is no way she could have seen Tom Riddle in his memory form, or know what Ginny was writing in Tom Riddle's diary. Why was Mrs. Norris targeted as a Basilisk victim? What did Tom Riddle have to gain by killing or petrifying Mrs. Norris?
★ I prefer a canon-based answer if possible (the Harry Potter novels, the three supplemental books, quotes from J.K. Rowling, or Pottermore information) and do not prefer an answer from either the HP Wikia or the Wikipedia.