Right Hand Free
There is (likely) nothing wrong with you. Don’t think too much why your soldier partner refuses to hold hands. It is probably because of something they learned in the military. Soldiers simply do not like to keep their dominant hand, be it left or right, occupied.
Hands In Pockets
There is something else that soldiers rarely do. You will not find them with their hands in their pockets! Again, they like to keep their dominant hand free. It is even better when both of their hands are unrestrained and available. When they are adopting their power stance, they will typically have their hands resting on their hips instead.