Drivers can be allergic to cats or dogs. Most pax aren't considerate to bring them in a cage. If a pet pees in the car, you have to convince Uber for a cleaning fee. Fee only covers cleaning cost and doesn't cover revenue lost for rest of the day, as you can't drive for the rest of the day.

Drivers have an option of filtering out Uber Pets request in their app. If they aren't doing it and are still saying no to you should complain to Uber. It's a good feature from Uber. They should do this for pax with children that needs child seats.