For a long time, ornithologists almost universally used the biological species concept (BSC). This definition of "species" is based on species being reproductively isolated from each other. Under this definition, distinctive geographical forms of the same "kind" of bird are usually lumped as one species. This is because the geographic forms interbreed (or probably would, if they had the chance) where they intersect on the map. The problem with this definition is slightly different, geographically-isolated, forms rarely present us with "tests" of their willingness to interbreed. According to to adherents of the BSC, if the forms are only slightly different, they would probably interbreed if given the chance. Thus, they should be considered the same species. However, proponents of the BSC also say that because two things rarely interbreed (and produce viable hybrids) doesn't mean they belong to the same species. For example, wolves and coyotes (there's no educated disagreement that these are different species) can mate and have fertile and healthy pups.
The phylogenetic species concept (PSC) says that diagnosable geographic forms of the same basic "kind" of bird should be treated as distinct species. This is because these forms have evolved separately, and have unique evolutionary histories. The PSC is gaining favor because there is no worry about whether slightly-different geeographic forms might interbreed. If they don't, for whatever reason (for example, migration to different breeding areas), they are full species. Obviously, the PSC is less restrictive than the the BSC. There would be many more species of birds under the PSC than under the BSC.
The debate over how species should be defined will continue as long as people are allowed to think freely. Perhaps the argument is rhetorical, because every kind of organism presents a unique situation. It is possiblew that neither definition can be applied consistently in nature.
The different kinds of crossbills are also phylogenetic species. They are geneological/evolutionary units. They should not be lumped into one species becuase they have diagnostic vocal and morphological differences.