Full-Duplex Speech-to-Speech Large Language Models (LLMs) are foundational to natural human-computer interaction, enabling real-time spoken dialogue systems. However, benchmarking and modeling these models remains a fundamental challenge. We introduce FLEXI, the first benchmark for full-duplex LLM-human spoken interaction that explicitly incorporates model interruption in emergency scenarios. FLEXI systematically evaluates the latency, quality, and conversational effectiveness of real-time dialogue through six diverse human-LLM interaction scenarios, revealing significant gaps between open source and commercial models in emergency awareness, turn terminating, and interaction latency. Finally, we suggest that next token-pair prediction offers a promising path toward achieving truly seamless and human-like full-duplex interaction.