The reasoning being that as you slide “forward” in your seat, you’re actually pushing the boat backwards with your momentum, since you face backwards in the boat.
It always struck me as strange advice though, because in a race you’re trying to get high stroke rates (35+ strokes per minute) and there’s not a lot of time between strokes to move your seat. And if you have to move your seat from A to B, there’s no real free lunch: Work equals force times distance, so you’re going to impart the same amount of momentum into the boat whether you move the slide slowly or quickly… it’s just a matter of how much time that work is spread out over, and that really shouldn’t make a difference to the boat.
Watching rowing in the Olympics it doesn’t seem like they’re worried about this at all. They just move from the back to the front of their seat quickly and it’s not some obvious effort to be gradual about it.
There were other dubious bits of advice too, like pushing with your legs first, then torso, then arms, but if you try to actually do that in reality it feels extremely awkward. And watching the pros do it on TV it doesn’t seem like they’re doing anything like this.