Why can you move your arm muscles?

because that's how the body is built

If your speaking about your biceps, it's because they don't start and end on your arm. Bi (2) Ceps Brachii has 2 heads. One of which originates on the coracoid process of the scapula. Both heads cross the elbow and insert on the radius. Thus because muscle pulls bones closer together, creating flexion, or bending the elbow. Same goes for triceps. Three heads, the long head originating on the scapula the other two on the posterior humerus (back of the arm). They insert on the elbow. This allows for extension of the arm and straightening the arm after bending the elbow.

http://www.exrx.net/Muscles/TricepsBrachii.HTML