Federated learning (FL) is an emerging machine learning paradigm with immense potential to support advanced services and applications in future industries. However, when deployed over wireless communication systems, FL suffers from significant communication overhead, which can be alleviated by integrating over-the-air computation (AirComp). Despite its advantages, AirComp introduces learning inaccuracies due to the inherent randomness of wireless channels, which can degrade overall learning performance. To address this issue, this paper explores the integration of fluid antenna systems (FAS) into AirComp-based FL to enhance system robustness and efficiency. Fluid antennas offer dynamic spatial diversity by adaptively selecting antenna ports, thereby mitigating channel variations and improving signal aggregation. Specifically, we propose an antenna selection rule for fluid-antenna-equipped devices that optimally enhances learning robustness or training performance. Building on this, we develop a learning algorithm and provide a theoretical convergence analysis. The simulation results validate the effectiveness of fluid antennas in improving FL performance, demonstrating their potential as a key enabler for wireless AI applications.