This has been discussed elsewhere and previously, and is mentioned on our new rules signs, but merits greater prominence.

Pets are not typically allowed in halls and classrooms by professors. This is an in-character rule, not an out-of-character one. One PC, Karen De Arith, was once given special permission by Dumbledore to keep her wolf with her, because she depended so thoroughly on him. (But Snape still wouldn't allow it to attend Advanced Potions with her when she wanted to observe the class.)

Obviously, the pets can be very useful at times. But if characters insist on keeping pets following them around the school at all times, they should expect to face reprimands and even punishments by certain teachers and members of the staff.