It's a matter of mechanical leverage. When you apply a force to the pedal perpendicular to the crank arm, the result is a moment (torque) equal to the product of the applied force and the crank arm length. This applied moment is resisted by an equal and opposite moment which is equal to the product of the chain tension force and the radius of the chainring. The chainring radius is directly proportional to the number of teeth on the chainring, which form the circumference of the chainring. Therefore, the tension in the chain is inversely proportional to the size of the chainring, and a smaller chainring size will equate to a larger tension force in the chain.