I don't know if this is an actual bug or not, but whenever I'm trying to complete the battle portion of the tutorial, it tells me my pet is busy, although I don't think it should be (and it doesn't say why so I can't check). 

Thanks for reporting.

This happened because you got a pet from another user. We didn't take into account this variant, so there was a mess with who should receive a challenge from the tutorial pet. The gifted pet was returned back to RushingWolf, I'll ask her to send it to you once again after you finish the tutorial.

Try to continue the tutorial now please.

Sorry for the inconvenience.