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This study examined competence as a moderator to resolve inconsistent findings on parental involvement and achievement goals among 517 Korean high school students. Using latent moderated mediation analysis, we found that parental achievement pressure comprised two distinct factors: achievement-oriented pressure and coercive pressure. Achievement-oriented pressure, when moderated by high competence, facilitated adaptive mastery and performance-approach goal formation, leading to better academic outcomes and reduced burnout. However, for low-competence students, achievement-oriented pressure showed no significant effects on adaptive goals. In contrast, coercive pressure, characterized by control, relative comparison, and excessive expectations, consistently predicted maladaptive performance-avoidance goals regardless of students' competence levels. These findings highlight the importance of considering both pressure types and individual competence when understanding achievement motivation in family contexts.