Social skills such as negotiation and leadership are crucial for personal and professional success in today's interconnected world. However, scalable and effective training remains a significant challenge due to the scarcity of expert coaching. In this paper, we introduce SocialCoach, a holistic LLM-powered agentic tutoring system for personalized social skill development at scale. First, SocialCoach automatically constructs a pedagogically-grounded, theory-to-practice knowledge corpus from diverse expert sources, leveraging a multi-agent pipeline. Second, to personalize the learning journey, it employs an adaptive practice scheduling module that follows a prescription-retrieval-adaptation process. To maximize the long-term learning experience while overcoming the cold-start problem, this policy is optimized within a learner simulation environment through reinforcement learning. Finally, SocialCoach integrates immersive, goal-driven practice, causality-driven proficiency assessment and knowledge-grounded, reflective tutoring to help address the knowing-doing gap. We deploy it in our product, EQoach, and conduct extensive experiments. The results show that SocialCoach improves simulated pathway quality and judge-rated tutoring quality over baseline approaches, while early user feedback indicates strong perceived engagement and usefulness. These findings suggest a practical architecture for personalized and gamified pedagogical platforms on soft skill learning.