As compared to continuing-generation students, first-generation students are struggling more at university. In the present article, we question the unconditional nature of such a phenomenon and argue that it depends on structural competition. Indeed, most academic departments use harsh selection procedure all throughout the curriculum, fostering between-student competition. In these departments, first-generation students tend to suffer from a lack of student-institution fit, that is, inconsistencies with the competitive institution's culture, practices, and identity. However, one might contend that in less competitive academic departments continuing-generation students might be the ones experiencing a lack of fit. Using a cross-sectional design, we investigated the consequences of such a context- and category-dependent lack of fit on the endorsement of scholastically adaptive goals. We surveyed N = 378 first- and continuing-generation students from either a more competitive or a less competitive department in their first or final year of bachelor's study. In the more competitive department, first-to-third year decrease of mastery goals (i.e., the desire to learn) was found to be steeper for first- than for continuing-generation students. In the less competitive department, the reversed pattern was found. Moreover, first-to-third year decrease of performance goals (i.e., the desire to outperform others) was found to be steeper within the less competitive department but did not depend on social class. This single-site preliminary research highlights the need to take the academic context into account when studying the social class graduation gap.