A primary difference is the connotation of the phrases. While "be good at" is a positive way to talk about one's skills, "be good for" is negative and insinuates that someone is being used for others despite how they feel about it. Here are some example sentences for both: "He was really good at cleaning!" vs. "He's only good for wiping dirty floors." "I think I'm pretty good at math." vs. "My grades have been getting worse... What am I even good for?" "Mom is really good at making lasagna!" vs. "Mom isn't good for anything besides cooking dinner." I hope that helps ^ ^

The difference is in denotation rather than connotstion. 'Good at' describes a person's abilities, such as speaking English or driving. 'Good for' describes usefulness for a purpose, and can be used for people, but also anything else. For example, I am good at speaking English, but not good at writing. My car is good for short journeys but not good for touring. In your example, only 'at' is appropriate. In both of Emma's examples she uses 'good for' to question her and her mother's usefulness but, as Michael points out, people and things can be useful as well as useless. There are a couple of special uses of 'good for' which add to the usual meaning: A good-for-nothing is a person who is completely useless; sadly my Dad is a good-for-nothing. We can use it as an adjective as well. To be good for means 'able and willing to give or lend'; this might apply only to BrEng, but it is always worth knowing somebody who is good for lunch, or good for £50.