@SophistiCat try this yourself try to join one of your hand with another by halving the distance , you will never reach your hand. thats the reason i discussed deceleration . halving the distance at every instant means you are decelerating instantaneously. if we do that we would never ever reach our other hand.

distance is forever related to velocity if taken in context with motion

Well, in easy words to me the whole paradox is asked wrongly, if we go into the deep logics we can see that if we clap our hands together , we our moving with accelerating velocity or in a constant velocity not in an instantaneous decelerating velocity . according to the paradox if we have our distance every time we will never reach the end and that is true. but in normal case we never half our distance or velocity instantaneously .So that is the reason our hands meet in the end.