Problem with stablingFollow

I'm trying to stable my pet for the first time. What happenned was I went to a stable master, bought a slot for 5s, and dragged my current pet into the slot. So far so good. So then I go out and try to tame another beast. I get the message "You already have a pet". Huh? So I call my pet and she shows up! I go back to the stable master and try to stable my pet again (the window shows that my pet is in one of the slots). When I leave the stable master my pet is still with me. I can't get my pet to stable. Furthermore, my level 20 pet who was my "best friend" is now "rebellious". Can anyone help me with this?

Thanks.