Although ample evidence exists that parenting is associated with children’s subjective well-being, researchers have not yet empirically examined the potential mechanism of this relationship. In this study, we consider emotional intelligence and cognitive flexibility as crucial capacities that could mediate the relationships between various parenting strategies (e.g., authoritative and authoritarian parenting) and young adults’ well-being (e.g., a high level of life satisfaction and lower levels of mental disorders). We collected survey data from 439 Taiwanese young adults aged 18 through 24. Via structural equation modeling analysis, we found that (a) authoritative parenting positively relates to young adults’ life satisfaction and negatively relates to their mental disorders, whereas authoritarian parenting positively relates to their mental disorders; (b) emotional intelligence mediates the relationship between authoritative parenting and young adults’ life satisfaction; and (c) cognitive flexibility mediates the relationship between authoritative and authoritarian parenting and young adults’ mental disorders. These results highlight the importance of democratic, warm, and responsive parenting that helps shape young adults’ cognitive flexibility, emotional intelligence, and subjective well-being.