Why do sabre fencers hop and bounce forward instead of just advancing like foilists do?

Mostly because sabre bans the flèche and crossing your feet forward, and the hop is how sabre fencers cover ground fast without breaking that rule. The USA Fencing rulebook, following the FIE, forbids the flèche and any forward movement in which the rear foot completely passes the front foot. It is a yellow card, any touch the offender scores is annulled, and a correctly made touch by the opponent still counts. Foil and épée have no such ban. Flèches and crossing steps are legal there, although in foil a run of crossing steps counts only as preparation, not as an attack.

The hop suits sabre because you can score with the edge and flat of the blade, not just the point, and the target is everything above the hips, including the arms and mask. An attacker in the air can land a cut the instant the defender commits, with no need to fix a point long enough for a tip to register. The bounce also breaks rhythm and keeps the legs loaded for a sudden finish. Its big cousin is the flunge, a flying lunge that replaced the flèche in sabre. Some foilists hop too now, but finishing from the air with the point is much harder.

Sabre uses right-of-way like foil, so the fencer who starts a proper attack has priority, but it is read at high speed. When both fencers start together in the middle, referees look hard at who committed first, and the feet often decide it. On a long marching attack, the attacker gets plenty of room to keep moving, hopping and adjusting the arm as long as they keep genuinely going forward. The moment they clearly stop or pull back, the defender can take over, and the call is often attack in preparation. Where exactly a stall becomes a stop is debated even among top referees.

Against a hopper, remember that a fencer in the air cannot change direction. Lunging into a forward hop is usually a mistake, because they just extend and finish with priority. Instead, stay close enough to be a threat and use your own footwork to draw their finish at a moment you choose. Then pull distance so they miss and hit back, or parry and riposte. If they start checking back or stalling, be ready to take over with a sharp, accelerating attack. Ask your coach to drill these responses, because the timing is learned by feel far more than by counting steps.