Every recipe about searing duck breasts I've seen says that you should score the breasts cutting through the skin, but not too deep: you should avoid cutting into the meat. I do follow this instruction but don't completely understand why. What harm could be done if I cut through the meat, just a little? What exactly should I avoid?
The little bit (about 4 - 5 grams after cooking) of fat in the breast itself will render out faster, and you could end up with a dryer over-crispy duck breast by the time it's done in the center. A tiny ding shouldn't present a problem, but if you actually get the whole or most of the edge of the blade into the breast, you'll have to pay close attention to heat as you cook it. If you score it that deep, you're probably better off poaching it in butter after searing.
The juices in the breast make it moist, and you definitely don't want to lose those either, but that tiny bit of fat in the breast once you've rendered out what's in the skin makes it delicious. You really want to keep that in.