The truth of the matter is that every bird that you refuse or fail to breed has in effect been culled. The reason behind this failure to breed is besides the point.
Exactly - the word "cull" has more meaning than simply to kill -- any selective breeding program (of any species) involves culling - and those "culls" can be killed or allowed to mature and live out their days- they just aren't used in the breeding program. To cull is merely to select.