In my American experience, you are correct that they are opposites. However, to be poor at, is not used very often. We would be more likely to say: not good at... Perhaps it is generational too. To be poor at feels a bit old-fashioned to me.

Hi Miki, Hi, when I studied English for exam to enter the high school, I was taught that the reverse of "be good at" was "be poor at". Do native speakers of English say like this? That is correct. For example, "John is good in Science." or "Judy is poor in English". In this context, the word "poor" does not refer to material wealth. It means to display a lack of proficiency in English. I tend to agree with Susanne. I remember my primary school teacher using this adjective when she wrote on my report card. I seldom hear it anymore though the meaning remains. Hope this helps. Cheers, Lance

In our case in Philippines, we used "be poor at" as an antonym to "be good at" Good in this situation is not used as an antonym of bad, but it means that you have the qualities required for something. That's the reason why "be poor at" is its antonym, or the opposite. "be poor at" means you don't have the necessary qualities required. I hope my explanation is easy to understand :)