I posted this in the general section but also thought it should go in the Cockatoos subforum - I previously hadn't know the biological differences as to why Cockatoos are classified outside of the Psittacidae family.

This relates back to a post from awhile ago where we were discussing parrot classifications - and one question was why the Cockatoos are classified under a different category than the rest of the Parrot family. Today I came across an article which explains classifications fairly well:

Phylogeny

The phylogeny of the parrots is still under investigation, and no definite answers are available for entire sections. The classifications as presented reflects the current status, and are subject to change when new studies resolve some of the open questions. For that reason, this classification should be treated as preliminary.

The Psittaciformes are generally considered to consist of two major living lineages of family rank: the true parrots (Psittacidae) and the cockatoos (Cacatuidae). The Cacatuidae are quite distinct, having a movable headcrest, different arrangement of the carotid arteries, a gall bladder, differences in the skull bones, and lack the Dyck texture feathers which, in the Psittacidae, scatters light in such a way as to produce the vibrant colours of so many parrots. However, the actual situation may be more complex (see below).

While understanding of the relationships between subgroups of true parrots — for example, the one containing the Grey Parrot vs. the relatives of the budgerigar — are rather well resolved and knowledge of relationships between species has much improved in the last years, it is still a matter of dispute whether the distinct lineages of true parrots should be considered subfamilies or tribes. Due to parrot fossils and molecular divergence date estimates providing insufficient data to properly resolve when exactly the major diversification and divergence periods in parrot evolution took place, it is difficult to determine how distinct the various lineages are really from each other, and how fast and radically they were changed by evolution.

Lorikeets were previously regarded as a third family Loriidae, though now most often considered a subfamily of the Psittacidae. Others lump all Psittaciformes into one giant family. The present majority view is that they are distinct enough to warrant subfamily status, but some consider the quite pronounced differences not evidence of a uniquely deep evolutionary split but rather not different quantitatively from the differences between more closely related lineages. Biogeography suggests that the lorikeets are best considered a uniquely distinct lineage, not as divergent as cockatoos maybe, but still standing apart from other psittacids.

Recent molecular studies, such as that of mtDNA in 1998, or the sex chromosome spindlin gene in 2005, find the relationships of the main lineages of living parrots to be for the most part unresolvable with any confidence. An unexpected result was that according to the spindlin sequence data, the only major divergence among living parrots that could be reliably positioned in the calculated phylogenies occurred between some New Zealand parrots - Kakapo, Kākā and Kea - and the remaining psittaciformes.

The case for distinctness of at least the nestorines seems to be fairly complete by now. Its position - with or without the kakapo - and ancient age as suggested by the molecular data is at odds with the fossil record though, as it would require an absurdly high degree of homoplasy and a decidedly non-parsimonious character distribution in living parrots. As the study relies upon an obsolete molecular clock model uncalibrated by material evidence, the results are highly spurious. The scenario of Miyaki et al. (1998), while less complete (and excluding the kakapo) agrees better, though not completely, with the material evidence. Again, an unreliable molecular clock model was used.

While the latter two seem indeed to constitute a distinct lineage, placement of the kakapo with these is contradicted by mtDNA cytochrome b sequence data. In any case, the major lineages of psittacines seem indeed to represent distinct clades, but their relationship among them is not well resolvable by the present molecular data. They appear to have radiated throughout a fairly limited timespan, approximately during the Eocene. One finding of major importance is that neither cockatoos nor lories seem to be as distinct from other major parrot lineages as they are usually assumed to be.

The site below is where this article came from and has more interesting information:
parrots - Information from Reference.com

Very interesting to note that these classifications are by no means cast in stone, and are in fact in a state of flux. Yet another reminder about how little we truly understand yet about these fascinating creatures!