The streeler is a giant snail that changes color every hour, and deposits a trail of venom as it moves that kills and shrivels all vegetation over which it passes, and which can kill horklumps. It is often kept as a pet (FB).
Although native to Africa, the streeler has been successfully bred in Europe, Asia and the Americas (FB).
A thirteen-year-old Newt Scamander kept a tank of streelers, along with some other creatures, in a cupboard at Hogwarts (CG).
streel (from Irish straoillim, trail along the ground) = Eng. to trail on the ground or float at length; when speaking of a person, to wander aimlessly [NSOED]
Streelers sound fascinating, but it isn't clear whether their venom affects humans. Seeing that many keep them as pets, we can assume not, since who'd keep a pet that would likely kill them in their sleep? (Don't answer that.) But I can see why they aren't on the list of approved school pets. I don't think Professor Sprout would be too pleased if one of these got near her 'classroom.'