the voltmeter must be connected in parallel to the resistor to read the potential difference across the resistor

Voltmeter has very high resistance to ensure that it's connection do not change the flow of current in the circuit. Now if it is connected in series then no current will be there in the circuit due to its high resistance. Hence it is connected in parallel to the load across which potential difference is to be measured.

Also the voltage in the parallel connection is constant; therefore we will not get any error while measuring the voltage across resistor.