Theory of Relativity

2 objects moving at the same speed in the same direction are, for all intents and purposes, standing still relative to each other.

It thus follows that if something is coming towards you, say a ball in flight, you can create more time to catch it accurately by moving in the same direction in which it is flying as you set up the catch.
Same with merging into traffic - get up to the same speed as the traffic and you have much more time to choose where to merge, and less adjustment you need to make to blend in.

Moving at the same speed as someone makes amazing things possible, especially if you also have the ability to modulate your own speed, in other words accelerate and decelerate so precisely that your changes in speed are close to imperceptible.

Other benefits -
- Our prey reflex is triggered by fast and jerky movements .. which is why predators move so smoothly and stealthily until they are in range to pounce. Move smoothly and you will be less visible, especially if you blend with your opponent's speed.
- Fast acceleration ans deceleration are more volatile to control, think catching a fast ball, or aiming to shoot.
- The smaller the differential, the more control is possible.