Implementations of Big Data analysis are reshaping society. The novel ways mathematics operate in society warrants new efforts for mathematics education, both in teaching the new technology and in providing an ethical and critical awareness of its implications. This interview study investigates pre-service teachers' ethical reasoning in data science contexts, focusing on aspects of access to the data that underpin the technology. Findings show that pre-service teachers offer a wide array of ethical arguments related to access to data, that informs their effort to think critically on oppressive situations. However, there is also an indication that their reasoning can be limited by lacking understanding of the related data science methodology, implying that mathematics teacher education should encompass more of this.