Big Stick ideology, Big Stick diplomacy, or Big Stick policy refers to U.S. President Theodore Roosevelt’s foreign policy: "speak softly, and carry a big stick." Roosevelt described his style of foreign policy as "the exercise of intelligent forethought and of decisive action sufficiently far in advance of any likely crisis"
The point of this scene was to emphasize that though Earth may not be as advanced as the Goul'd in the sense of space travel and medicine, they do have great training and sufficient equipment.