A matter of accuracy
Medication dosage often needs precision for the illness or to make the meds last.
There is a problem using common kitchen measures to do so. If i want a kid to get 5ml of med/dose, i could write for a teaspoon, but some common teaspoons would measure out 3.5ml and some 7. Over time i could under or over medicate the patient. Millileters are easily measured by syringes or droppers & assure accuracy.