Why do some minority groups succeed in preserving their cultural identity despite the repressive assimilation efforts of the state, while others fail this struggle and risk cultural extinction? This paper explores the dynamics of cultural transmission and minority identity preservation amid nation-building efforts, combining theoretical modeling with a historical case study analysis of Turkish Kurdistan. I analyze the competing forces between parental socialization within minority groups and state-driven efforts to homogenize the population. The state, aiming to promote national unity, employs various strategies---from language prohibition to massacres and genocide---that challenge the transmission of minority traits. Simultaneously, minority parents invest in transmitting their cultural identity to future generations. My model examines how these interactions shape the cultural landscape, leading to either cultural diversity or homogenization. My model demonstrates that even if there are no representatives of the cultural majority trait initially present in the population, the nation-building effort is sufficient to shift the system toward a non-degenerate distribution. It also demonstrates that this effort is not sufficient to fully homogenize the population. The cultural minority can increase its effort to preserve its distinctiveness, thereby resisting the nation-building effort. Drawing on historical evidence from Turkish Kurdistan, I demonstrate how the Kurdish population not only resisted the nation-building efforts of a repressive authoritarian state but also mobilized en masse in the struggle for cultural and political autonomy. I argue that Kurdish cultural elements transmitted through endogenous community effort were instrumental in preserving Kurdish identity and shaping minority responses to assimilation policies.