There is a distinction to be made that is easily overlooked: training versus performing. When the Special Forces are performing, obviously they are not going at a slow pace. It takes full speed movements to breach a door, clear a room, secure hostiles, and remove friendlies. None of this goes slow, as the situation does not allow slow.
However, the training does go from a slow speed to performance speed. Another related military mantra is “crawl, walk, run.” Start by focusing on individual steps (slow: this is often accomplished by way of lecture or simulated sandbox training), move to rehearsing at half-speed “walking,” to internalize the movements and build muscle memory, then “run” to push everything up to the speed needed for the mission.
Perhaps a nice illustration of the importance of all of this is to take a combat situation of a squad clearing a building with no knowledge of what’s inside, and then imagine that your only focal point is to watch where each weapon is pointing, start to finish. Without “crawl, walk, run” training, without “slow is smooth, smooth is fast,” you would see it repeatedly happening that weapons are sweeping across fellow soldiers, friendlies, even hostiles that are not an imminent threat, with the possibility of unintentionally firing the weapon in the heat of the moment that results in a casualty. Training will explicitly address this issue to help reduce the likeliness of it happening.
Any number of other illustrations could be drawn, from practicing an instrument, penmanship, keyboard speed, defensive driving, even taking your toddler into the public where opportunities for bumps and bruises abound!