Teddy Roosevelt's big stick comment exemplifies the dual role of the US President.
The US President is the Head of State and so must be the chief diplomat. But they are also the head of the military.
So, a President must know when to use diplomacy and when to use the military.
Roosevelt's comments are often misunderstood and I agree with the actual meaning. It is important for a President to speak diplomatically. That is the first step before using the military.