Why is it dangerous to touch the terminals of a high-voltage capacitor even after the voltage source that charged the capacitor is disconnected from the capacitor?

Because the capacitor will deliver all its charge to the lower potential as soon as the circuit is completed and give a direct current electrocution to the person.

Explanation:

It is dangerous to touch the terminals of a high voltage capacitor even after the voltage source that charged the capacitor is disconnected form the capacitor because a capacitor stores the charge according to its capacitance and delivers the current when the circuit is having a lower voltage.

Hence when someone touches the terminals of a capacitor simultaneously the the person completes the circuit of the of the capacitor through her/his body and hence will feel the shock of direct current since there are opposite charges stored on each of the two plates of the capacitor. The direct current is more dangerous as it give a continuous shock of a constant magnitude until the whole charge is dissipated.