A fundamental law of mechanics is that a body free of external torques will preserve its angular momentum. However, that is not the same as the body's angular velocity. Roughly speaking, the angular momentum is the product of the angular velocity and the moment of inertia. If the body preserves its moment of inertia, then the angular velocity along with the angular momentum is preserved. However, if the body changes its moment of inertia, then the angular velocity must also change in the opposite direction to preserve the angular momentum. When the ice skater brings his or her arms in close to the torso, that has the effect of reducing the total moment of inertia of the skater, and consequently their angular velocity must increase to maintain a constant angular momentum.
To choose an extreme case, when a hiker ascends a mountain, that increases the total moment of inertia of the whole earth system including the humans on it by a tiny amount and it must consequently slow down its rotation rate with the day increasing in length by a tiny amount. However, as far as I am aware no-one has seriously worried about the effect mountain climbers have on the length of earth's day.
