Self-supervised neural machine translation (SSNMT) jointly learns to identify and select suitable training data from comparable (rather than parallel) corpora and to translate, in a way that the two tasks support each other in a virtuous circle. In this study, we provide an in-depth analysis of the sampling choices the SSNMT model makes during training. We show how, without it having been told to do so, the model self-selects samples of increasing (i) complexity and (ii) task-relevance in combination with (iii) performing a denoising curriculum. We observe that the dynamics of the mutual-supervision signals of both system internal representation types are vital for the extraction and translation performance. We show that in terms of the Gunning-Fog Readability index, SSNMT starts extracting and learning from Wikipedia data suitable for high school students and quickly moves towards content suitable for first year undergraduate students.