Federated learning (FL) in wireless networks is limited by straggler delays from unpredictable channel conditions. In this paper, we investigate the pinching-antenna system (PASS), which dynamically 'pinches' the radiator along a dielectric waveguide to shorten the worst links. In synchronous FL (SFL), we prove that PASS shortens the worst-link distance, and it increases the on-time completion probability in asynchronous FL (AFL). Accordingly, SFL exhibits stochastic dominance on round time, while AFL yields explicit latency and participation gains. We then pair physical-layer (PHY)-aware sampling with error-feedback compression and prove that pinching raises the minimum inclusion probability, thus shrinking both the sampling variability and compression-induced floors in a Lyapunov analysis. Simulations demonstrate consistent wall clock speedups and markedly shorter latency tails. By addressing stragglers at their PHY root, PASS complements higher-layer scheduling and accelerates wireless FL in both SFL and AFL.