Group recommendation systems play a pivotal role in supporting collective decisions across various contexts, from leisure activities to organizational team-building. Existing group recommendation approaches typically use either handcrafted aggregation rules (e.g. mean, least misery, weighted sum) or neural aggregation models (e.g. attention-based deep learning frameworks), yet both fall short in distinguishing leader-dominated from collaborative groups and often misrepresent true group preferences, especially when a single member disproportionately influences group choices. To address these limitations, we propose the Dual-stream Adaptive Leadership Identification (DALI) framework, which uniquely combines the symbolic reasoning capabilities of Large Language Models (LLMs) with neural network-based representation learning. Specifically, DALI introduces two key innovations: a dynamic rule generation module that autonomously formulates and evolves identification rules through iterative performance feedback, and a neuro-symbolic aggregation mechanism that concurrently employs symbolic reasoning to robustly recognize leadership groups and attention-based neural aggregation to accurately model collaborative group dynamics. Experiments conducted on the Mafengwo travel dataset confirm that DALI significantly improves recommendation accuracy compared to existing frameworks, highlighting its capability to dynamically adapt to complex, real-world group decision environments.