Muscles span joints, and their purpose is to affect movement of that joint. Typically a muscle's origin is the more fixed or stable point of attachment to bone, while the insertion is on the bone which moves when contraction or relaxation of that muscle occurs.
Usually with the muscles of the limbs we think of the more proximal end of the muscle as being the origin, and the distal end being the insertion, because muscle action tends to move bones more distal to the limb joints. For example, for movement of the elbow joint you can typically think of muscles originating on the humerus and inserting on the radius and ulna.
However the nomenclature is somewhat arbitrary, because one can in a sense reverse the origin and insertion by fixing the location of the more distal bone and moving the upper body. For example, by placing your forearm still on the table and moving your upper body, because of the nature of their action in this position you might consider the muscles of the elbow to originate on the radius/ulna and have their insertion on the humerus.
I suspect this is what is described in the book. The biceps brachii attaches to the scapula and radius. Depending on whether it is the forearm or the shoulder moving with respect to the elbow joint, the insertion and origin could be considered at either end of the muscle. It is not that the origin/insertion is always opposite for the right versus left limb.