What we are looking for in good running is adaptability. Stability, in the form of conscious muscular contraction, works against this, preventing the reflexive distribution of effort throughout the muscular system. Simply put, if you hold your muscles – for example, to create “core stability”, the muscles you hold will not adapt as easily as they might do without your interference, and further, the stability you create in the muscles you hold will both increase the effort required to move other parts, and block the efficient transfer of work to surrounding muscles.
Don’t take my word for it; here is a detailed study in pdf:
“The myth of core stability” Lederman
Stability is the enemy of coordination
The first, and often misunderstood, concept is posture. Most people, when considering posture, imagine that good posture is right positioning of body parts. This kind of misconception can lead to many problems, resulting in effortful running and increased injury. If you try to position your body parts, you will interfere with the work of posture.
The postural system allows the whole body to adapt constantly to forces both external and internal, in such a manner that effort is efficiently distributed throughout the body. This cannot occur if there is positioning – if, for example, the head is held in a certain position, or if the hands or elbows are maintained in positions.
When the postural systems are working well, that is to say, when they are not interfered with by positioning, we can see that the simple act of raising a hand involves the entire body. First, the vestibular (or balance) system will anticipate and adapt for the change in global balance that will occur when a limb is moved. This means that upper neck muscles will move or release the head’s weight to initiate postural change (see: The Head-Neck Sensory Motor System, ed. Alain Berthoz). As the arm moves, let’s say forwards to shake someone’s hand, muscles will anchor the shoulder blade so that it does not slide upwards and forwards with the arm (though it will need to move constantly during the arm action). The knees, ankles and hips will move, to allow the body’s weight to shift rearwards to compensate for the forward movement of the arm.
This is a huge oversimplification. Even when the body is not moved, it is moving, for, without movement there could be no balance or proprioception (the feeling of relative positioning of body parts, which requires lengthening and shortening of muscles). If the fluid in the inner ear is not moved, there is no signal. So opposing muscles are constantly lengthening and shortening in a gentle alternance, which creates sway, and allows the inner ear to measure acceleration and deceleration.