This study examines how the relationship between social media discourse and offline confrontations in social movements, focusing on the "Black Lives Matter" (BLM) protests following George Floyd's death in 2020. While social media's role in facilitating social movements is well-documented, its relationship with offline confrontations remains understudied. To bridge this gap, we curated a dataset comprising 108,443 Facebook posts and 1,406 offline BLM protest events. Our analysis categorized online media framing into "consonance" (alignment) and "dissonance" (misalignment) with the perspectives of different involved parties. Our findings indicate a reciprocal relationship between online activism support and offline confrontational occurrences. Online support for the BLM, in particular, was associated with less property damage and fewer confrontational protests in the days that followed. Conversely, offline confrontations amplified online support for the protesters. By illuminating this dynamic, we highlight the multifaceted influence of social media on social movements. Not only does it serve as a platform for information dissemination and mobilization but also plays a pivotal role in shaping public discourse about offline confrontations.