Why should a voltmeter have a very high resistance?

Hint: Here you need to know that high resistance restricts the current to pass through it giving more accurate reading of the voltage. Knowing this will solve your problem.

Complete step-by-step answer:
A voltmeter is a device used to measure the electrical potential difference between two points of an electrical circuit. Analog voltmeters shift the pointer around a range in accordance to the voltage of the circuit; digital voltmeters show the voltage by means of an analog-to - digital converter.
A voltmeter measures the difference in voltage between the two different points (say, on opposite sides of a resistor), but it does not adjust the amount of current passing between these two points through the device. It will therefore have very high resistance, so that it does not draw current through it.

Note: The lower the resistance the voltmeter puts across the load, the more wrong the reading will be on the voltmeter. The best voltmeter will have such a high resistance that it will not significantly change the current in the circuit. Good, modern voltmeters have several megohm input resistance. Ideally, an ammeter should have zero resistance and a voltmeter infinite resistance to give correct readings.