Memristors are prominent passive circuit elements with promising futures for energy-efficient in-memory processing and revolutionary neuromorphic computation. State-of-the-art memristors based on two-dimensional (2D) materials exhibit enhanced tunability, scalability and electrical reliability. However, the fundamental of the switching is yet to be clarified before they can meet industrial standards in terms of endurance, variability, resistance ratio, and scalability. This new physical simulator based on the kinetic Monte Carlo (kMC) algorithm reproduces the defect migration process in 2D materials and sheds light on the operation of 2D memristors. The present work employs the simulator to study a two-dimensional 2H-MoS2 planar resistive switching (RS) device with an asymmetric defect concentration introduced by ion irradiation. The simulations unveil the non-filamentary RS process and propose routes to optimize the device's performance. For instance, the resistance ratio can be increased by 53% by controlling the concentration and distribution of defects, while the variability can be reduced by 55% by increasing 5-fold the device size from 10 to 50 nm. Our simulator also explains the trade-offs between the resistance ratio and variability, resistance ratio and scalability, and variability and scalability. Overall, the simulator may enable an understanding and optimization of devices to expedite cutting-edge applications.