The military uses "intention" rather than "I will" because they understand that no plan survives contact with the enemy. It is also higher level so that when exhausted, stressed subordinates find themselves in life threatening circumstances the most important thing they need to remember is the intent. If they forget steps 1-5 of the plan but recall the intent they can't go that badly wrong in using their initiative.
There's also the distinction between specific orders - "you are to". Knowing the commander's intent, and his commander's intent (known as 1 Up and 2 Up) enables Mission Command, the concept of giving latitude to subordinates to achieve the mission in the best way possible within the confines and direction given to them.
Finally there's the ritual of it, NATO forces expect to operate within multi-national structures where English won't be a first language. There is a "NATO sequence of orders" which should be roughly followed. It means everyone knows the structure of what is coming up and when in the brief - so you don't get people asking questions about equipment when the limitations are being explained, they know that comes later. Opening, especially from a junior officer, with "my intention is" is essentially like having a schema definition at the start of a document - it defines the structure of what is coming for those who are going to be parsing it.
