RBCs pick up oxygen from lungs and deliver it to the tissues: why is it not the other way around?
Red blood cells can absorb oxygen from areas with higher concentration of oxygen. Red blood cells, on the other hand, can release oxygen in areas with lower concentration of oxygen.
Our body is designed with a purpose.
Red blood cells are loaded with hemoglobin, that acts as a transport protein for oxygen. Affinity of hemoglobin for oxygen will increase with increasing partial pressure of oxygen.
Alveoli are continuously supplied with fresh air when we breathe (carbon di oxide is also continuously breathed out): hence partial pressure of oxygen in lungs is higher than that in the pulmonary blood capillaries. Diffusion of oxygen thus takes place from lungs to capillaries.
In living tissues, oxygen is used up and carbon di oxide is generated due to cellular (aerobic) respiration. Low partial pressure of oxygen in tissues means oxygen will diffuse out from surrounding systemic capillaries (where partial pressure of oxygen is comparatively higher) in the tissue space.
From the above discussion it will be clear why the opposite will never take place in a livung body.