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Producing code of good quality is an essential skill in software development. Code quality is an aspect of software quality that concerns the directly observable properties of code, such as decomposition, modularization, and code flow. Code quality can often be improved by means of code refactoring -- an internal change made to code that does not alter its observable behavior. According to the ACM/IEEE-CS/AAAI Computer Science Curricula 2023, code refactoring and code quality are core topics in software engineering education. However, studies show that students often produce code with persistent quality issues. Therefore, it is important to understand what problems students experience when trying to identify and fix code quality issues. In a prior study, we identified a number of student misconceptions in method-level code refactoring. In this paper, we present the findings from a think-aloud study conducted to investigate what students think when working on method-level refactoring exercises. We use grounded theory to identify and classify student reasoning. As a result of the analysis, we identify a set of eight reasons given by students to refactor code, which either concerns the presence of code quality issues, the improvement of software quality attributes, or code semantics. We also analyze which quality issues are identified by students, and to which reasonings these quality issues are related. We found that experienced students reason more often about code quality attributes rather than pointing at a problem they see in the code. Students were able to remove code quality issues in most cases. However, they often overlooked particular issues, such as the presence of a method with multiple responsibilities or the use of a less suitable loop structure.