In the case of a skater however there is indeed conservation of momentum and radial motion of the arms makes the skater either have an angular acceleration or deceleration. This often used analogy of a spinning skater is completely misleading and leading jaridyard and likely others to mistakenly starting to reverse cause and effect. For a golfer action is from the inside-out and for a spinning skater it is from the outside-in. Rotational mechanics isn't easy, rather confusing, and should be treated with care.
If I jump from a big ocean vessel there is an equal and opposing action and reaction force at work. However the mass of the large ship being so much larger it experiences negligible deceleration. However if I try to jump out of a small tiny rowing boat it is a complete different story. It is to be expected that this sort of mistake is not usually made more than once.
It just so happens that from the ground up as in a whip a golfer goes from heavier to lighter segments. It is only for these condition that the velocity multiplication effect of a kinetic chain can be effective.