We rely on arguments in our daily lives to deliver our opinions and base them on evidence, making them more convincing in turn. However, finding and formulating arguments can be challenging. In this work, we train a language model for argument generation that can be controlled on a fine-grained level to generate sentence-level arguments for a given topic, stance, and aspect. We define argument aspect detection as a necessary method to allow this fine-granular control and crowdsource a dataset with 5,032 arguments annotated with aspects. Our evaluation shows that our generation model is able to generate high-quality, aspect-specific arguments. Moreover, these arguments can be used to improve the performance of stance detection models via data augmentation and to generate counter-arguments. We publish all datasets and code to fine-tune the language model.