This is a hard one, there are little disadvantages of classifying organisms, only the mistakes that can arise from it are often apparent.
As of right now during scientific times and proper research, it is often hard for us now and is nearly unheard of from classifying organisms incorrectly.
An example could be those of the ‘sloth bear’, in which it was originally cordoned off as being a relative of the sloths found in South America, due to just looking like them or having a few behaviours like them.
We now know they are distinct and are a bear of insectivorous nature.
We could also apply this same sort of thinking to Pandas of both kind, red and giant, in which even with the scientific expertise, we often struggle to classify as a species.
We could then draw from this that our own obsession with classifying and organising organisms into their own respective families is a disadvantage in itself.
Hope this helps.