We conducted molecular dynamics (MD) simulations in a binary Lennard-Jones system as a model system for molecular solutions and investigated the mechanism of liquid-liquid phase separation (LLPS), which has recently been recognized as a fundamental step in crystallization and organelle formation. Our simulation results showed that LLPS behavior varied drastically with the size ratio of solute to solvent molecules. Interestingly, increasing the size ratio can either facilitate or inhibit LLPS, depending on the combination of interaction strengths. We demonstrated that the unique behavior observed in MD simulation could be reasonably explained by the free energy barrier height calculated using our thermodynamic model based on the classical nucleation theory. Our model proved that the molecular size determines the change in number of interaction pairs through LLPS. Varying the size ratio changes the net number of solute-solvent and solvent-solvent interaction pairs that are either broken or newly generated per solute-solute pair generation, thereby inducing a complicated trend in LLPS depending on the interaction parameters. As smaller molecules have more interaction pairs per unit volume, their contribution is more dominant in the promotion of LLPS. Consequently, as the size ratio of the solute to the solvent increased, the LLPS mode changed from solute-related interaction-driven to solvent-related interaction-driven.