Non-polar solvents dissolve non-polar solutes due to favorable interactions at the molecular level. The principle of "like dissolves like" explains that non-polar solvents have similar molecular characteristics to non-polar solutes, allowing for effective interactions. These interactions create solvent-solute 'bonds' that facilitate the solute's integration into the solvent, resulting in the solute being completely surrounded and dissolved by the solvent molecules. This process highlights the importance of molecular compatibility in solubility.