If you’re a regular reader, you’ll note the recurring theme of "every animal (and person) is carrying multiple microbes that can harm you, given the right circumstances. Fortunately, the right circumstances don’t usually occur."
There are situations in which those risks increase, and understanding cost-benefit is a key aspect of disease prevention. Sometimes pet

Pasteurella multocida is a bacterium that is commonly found in various pet species. It typically inhabits the upper respiratory tract of healthy pets, although it is an important cause of respiratory disease in rabbits ("snuffles"). It is also a zoonotic pathogen, and human infections are sporadically reported. Most are associated with bites, mainly from cats.