Having very specific names for things is extremely important in scientific and technical disciplines. As such, almost every esoteric field has extremely specific and detailed rules for establishing technical names. These are frequently established by highly complex international boards over long periods of time and are about as byzantine as anything imaginable.
Three familiar examples of technical naming are the IUPAC rules used in Chemistry (wherein isopropyl alcohol becomes 2-propanol), the Nomina Anatomica used by those in the medical and related fields (by use of which the collarbone becomes the Os Clavicula), and the binomial taxonomic system for classifying animals and plants (which names a moo-cow a Bos taurus, unless it is the kind from Asia, in which case it is Bos indicus).
Among the chief reasons that scientists and technicians prefer these complex naming conventions over the more common names is a simple matter of precision. Common names are notoriously imprecise and may even be misleading. For example, the North American animal known as a ringtailed cat or civet cat is, in fact, not a civet nor a cat, but a close relative of the raccoon.
Furthermore, some of these names can encode a large amount of information. A chemist could tell very little from the common name propylacetylene, but with the IUPAC name 1-pentyne, could construct the structural formula of the compound.
Another issue with common names is purely linguistic. Many languages have their own common name for an animal, chemical compound, electronic component or what have you. As scientific and technical matters have become increasingly international, consistent names that can be used in many different lands have become more and more important.
Latin and Classical Greek are frequently used as a solution to the matter of language. These tongues were largely picked for the role that both have played in the development of many of the Western languages. Also, of course, both are considered to be languages of classical scholarship, so I suppose the choice is fairly reasonable (although I might add Arabic into the mix, but that's just an editorial comment).
Brady, James E., "General Chemistry," Third ed., (John Wiley, New York, 1982).
Taber's Cyclopedic Medical Dictionary, 19th edition (FA Davis, Philadelphia, 1997).