Pinching antennas are characterized by their capability to create strong line-of-sight connections and realize multi-antenna systems in a flexible manner. Existing works have demonstrated the significant potential of pinching antennas for physical layer design. The aim of this paper is to investigate how pinching antennas can be used to reshape the architecture of future networks. In particular, this paper is motivated by the key advantage of pinching antennas, which is to reconfigure the physical boundaries of wireless cells, and focuses on the impact of pinching antennas on traffic offloading. The models for traffic offloading and pinching antenna transmission are presented first. Then, two traffic offloading strategies are developed based on whether an offloading user releases its bandwidth in its original cell. An overall transmit power minimization problem is formulated, where the optimal solutions for the transmit powers and antenna locations are obtained. The presented simulation results demonstrate that the use of pinching antennas can efficiently support traffic offloading, yield low energy consumption, and achieve balanced cell resource utilization.