Why do you say due like due north before saying a direction?

Due in this form is refering to the four Cardinal (Main) points of the compass that bear a 90º angle to each other, North, South, East and West. You would never say, "Head due South West".

It is used because it is derived from the Word Due, meaning as it ought to be, as is fitting, to be observed or in Due course. Now as you can see Course is also a direction a ship would take, its easy then to make the leap that the Course a ship would be on is a heading of Due North.