My 7 year old's had an idea. When you are in the pet pavilion, you should be taken off your mount, so your pet is on display. They like to look at the other pets, and when someone is on a mount, they need to click on them and view their stats, which wouldn't be necessary if they were on their feet. It makes sense to me, you are working with your pet while in there, so why not showcase your pet? I'm usually off my mount while in there, and the time saved while 'riding' from one place to another is negligible compared to being on a mount.
Angus Firehammer - ancient (ALMOST epic) orthrus pet owner