Colleges and universities certainly want to encourage diversity and ensure access for individuals with disabilities. If you want to bring a seeing eye dog or cat to class, that will probably not be a problem. If you need a stuffed animal to be comfortable, that may be OK, too.
Nevertheless, professors and their institutions have to draw the line somewhere. Not only is having a seeing eye giraffe, elephant, or hippopotamus quite disruptive to the educational process; these also take up a great deal of space and, at least occasionally, cause significant damage to the buildings. Because of their obstructive qualities, these may also bring the institution out of compliance with fire and other emergency evacuation regulations. In terms of logistical concerns, those that are not properly house trained may cause serious littering problems and unpleasant odors that will interfere not only with your own learning, but also that of your classmates.