Metamaterial discovery seeks microstructured materials whose geometry induces targeted mechanical behavior. Existing inverse-design methods can efficiently generate candidates, but they typically require explicit numerical property targets and are less suitable for early-stage exploration, where researchers often begin with incomplete constraints and qualitative intents expressed in natural language. Large language models can interpret such intents, but they lack geometric awareness and physical property validity. To address this gap, we propose MetaSymbO, a multi-agent framework for language-guided Metamaterial discovery via Symbolic-driven latent evOlution. Specifically, MetaSymbO contains three agents: a Designer that interprets free-form design intents and retrieves a semantically consistent scaffold, a Generator that synthesizes candidate microstructures in a disentangled latent space, and a Supervisor that provides fast property-aware feedback for iterative refinement. To move beyond the limitations of reproducing known samples from literature and training data, we further introduce symbolic-driven latent evolution, which applies programmable operators over disentangled latent factors to compose, modify, and refine structures at inference time. Extensive experiments demonstrate that (i) MetaSymbO improves structural validity by up to 34% in symmetry and nearly 98% in periodicity compared to state-of-the-art baselines; (ii) MetaSymbO achieves about 6-7% higher language-guidance scores while maintaining superior structure novelty compared to advanced reasoning LLMs; (iii) qualitative analyses confirm the effectiveness of symbolic logic operators in enabling programmable semantic alignment; and (iv) realworld case studies on auxetic, high-stiffness metamaterial design further validate its practical capability.