Why it is Meine and not Mein?

Menschenkind is right. But I might add that "ganz gut" usually means "pretty good" not "quite good", with other adjectives it is different though. "ganz unmöglich" really means "quite impossible", with "ganz gut" the meaning of "ganz" has changed. To make it "quite good" you would say "sehr gut" or "wirklich gut".

Why is 'Meiner ist ganz gut' wrong?

I put 'thinking is quite good' because for some reason 'mine is quite good' didn't seem to make sense to me. lol