A header spans an opening and carries the load that the interrupted studs would otherwise have taken directly to the plate — floor loads, roof loads, and everything above. It is sized for that span and that load, so it has no surplus material to give away. Cutting it for a duct or a pipe removes section exactly where bending stress is highest, and unlike a joist there is no permitted-hole zone because the member is short, heavily loaded and often built up from multiple plies. The finding matters in interior walls as well as exterior ones, since interior bearing walls carry floor and roof loads too. As with any structural alteration, the inspector reports the penetration and refers evaluation, because whether the remaining section is adequate is a calculation.