Learning to control high-speed objects in dynamic environments represents a fundamental challenge in robotics. Table tennis serves as an ideal testbed for advancing robotic capabilities in dynamic environments. This task presents two fundamental challenges: it requires a high-precision vision system capable of accurately predicting ball trajectories under complex dynamics, and it necessitates intelligent control strategies to ensure precise ball striking to target regions. High-speed object manipulation typically demands advanced visual perception hardware capable of capturing rapid motion with exceptional temporal resolution. Drawing inspiration from Kahneman's dual-system theory, where fast intuitive processing complements slower deliberate reasoning, there exists an opportunity to develop more robust perception architectures that can handle high-speed dynamics while maintaining accuracy. To this end, we present \textit{\textbf{SpikePingpong}}, a novel system that integrates spike-based vision with imitation learning for high-precision robotic table tennis. We develop a Fast-Slow system architecture where System 1 provides rapid ball detection and preliminary trajectory prediction with millisecond-level responses, while System 2 employs spike-oriented neural calibration for precise hittable position corrections. For strategic ball striking, we introduce Imitation-based Motion Planning And Control Technology, which learns optimal robotic arm striking policies through demonstration-based learning. Experimental results demonstrate that \textit{\textbf{SpikePingpong}} achieves a remarkable 92\% success rate for 30 cm accuracy zones and 70\% in the more challenging 20 cm precision targeting. This work demonstrates the potential of Fast-Slow architectures for advancing robotic capabilities in time-critical manipulation tasks.