it's in the text menu to say 'good girl/boy' because it is considered Good Luck to encourage your pet - it is a wiz tradition. We all applaud our pets when they are doing well.
feeding pets extra stuff (seeds, gear, jewels, etc) before going into battle always seems to boost my pets may cast actions.
they like attention, so show the love it never hurts.
I see people say "Good boy/girl" whenever their pet helps them in battle so does that help the pet keep doing it?
That's something I've been curious about myself!! I have a Sea Dragon named Sasha who has the Spritely (May cast Sprite) talent, and I don't usually say the menu chat phrase "Good girl!" whenever she heals me because I figured it wouldn't make a difference.
However, one time I decided to say it just for the heck of it, and a round or two later she healed me again! So, I decided to say it again! Then in the next battle after that she healed me yet again! Sasha usually doesn't heal me that often, so I was really surprised!
It might just be a coincidence, but saying "Good boy/girl!" might make a difference! However, I don't know for sure because I'm not a developer for the game.