Better vs good?

I want to have a pen friend, hopefully a girl in her early twenties, with interests similar to mine. In my mind, she is someone who is interested in traveling, swimming, and playing table tennis. Besides, it would be better/good for her to have a pet dog as I have kept one at home for some time.

Which word should I choose? "better" or "good"? My exercisebook says only "better" is correct. So I am wondering why "good" is incorrect? Would you please tell me why?

Thank you.