One special branch in chemistry is allotted to compounds of only one element (carbon). Is it justified when there are more than 115 elements and their compounds but not with any special branches?
Carbon has a valency of four which helps in bonding with other atom or groups easier and adds to catenation. When one talks of Carbon's ability to bond, then Catenation property should come to your mind. Catenation is the linkage of atoms of the same element into longer chains. Catenation occurs most readily in carbon, which forms covalent bonds with other carbon atoms to form longer chains and structures. This is the reason for the presence of the vast number of organic compounds in nature. One such marvel is DNA! So, while studying chemistry, Carbon compounds form a class of peculiar natured compounds and the vast range of molecules and development of their own domain in their own scale might have made people feel that a separate category should be made for Carbon compounds because of their vastness and availability, also predominately manifestation of them in almost every thing, even life! In fact life became possible only because of Carbon, such is the importance. They have got their own nomenclature system in their domain.. Its really vast. The study of everything begins with Organic compounds first.. be it isomerism, medicinal reaction or anything. So, you may see, how important Carbon is. If you are a biology student, you must have learned about biomolecules.. DNA and gene pool, replication, transcription, translation, protein coding, defective proteins and some viral components and its lifecycle. Molecular basis of genetics is based on DNA and other organic compounds. That gives you thrilling experience to see how stuffs work and wonder about their importance and manifestation. Carbon is a wonder.