Why use milk in white sauce?
Well, white sauces are by their very definition milk or milk
product based sauces, rather than broth, stock, or say tomato based
sauces. Brown gravy or au jus are by definition based on beef
broth, beef stock or beef demiglace, whereas country gravy is a
milk based gravy, generally served with pork chops or chicken fried
steak. If you're asking why milk versus half and half versus light
or heavy cream, my guess is the recipe you are looking at wants
less fat than half and half or cream provide.