Composable architecture is often met with pushback due to its unfamiliarity, perceived complexity, potential time-consuming migration process, and fear of undoing existing work. To overcome these objections, it's essential to approach the transition incrementally, focusing on one business challenge at a time, and showcasing long-term cost savings through an investment analysis. By asking questions like "How much time are we spending on maintenance?" and "Could I (a developer) be working on more important projects?", you can navigate the monolith-is-fine conversation and demonstrate the value of composable architecture. Additionally, emphasizing that a migration doesn't require undoing existing work and that it's an opportunity to adapt to changing business needs can help alleviate concerns. By taking an incremental approach and highlighting the benefits of composable architecture, you can overcome pushback and successfully transition to a more flexible and scalable architecture.