Suppose I'm just standing somewhere and I move my hands. My body is the system. When I move my hands, it's not like the rest of my body has to be moved in the opposite direction. I can move my hands while keeping the rest of the body still. When the position of hands changes, the configuration of particles changes, hence the center of mass of my body accelerates. But a system shouldn't be able to exert net force on itself! In case of jumping, we don't create the jump force, instead it comes from the reaction force of the ground. But in the hand motion, we don't have to exert force on the ground, hence no reaction, no outside force. So, do living things create this force?
If you were floating in space, what you say would be true. However, here on earth, your feet are planted on the ground.
When you move your hand, the rest of your body does move in the opposite direction a little, especially at first. However, your body has a amazing mechanical control system. It will compenstate for the movement of your body and restore its initial position by changing how it pushes on the floor with the feet. This happens so well and is so automatic that you aren't usually aware of it unless you deliberately think about it.