Isn't astrobiology (the study of EARTH organisms) kind of an oxymoron ?

I think the GFAJ-1 bacterium substituting arsenic for phosphorous was recently found to be erroneous. Turned out there was still phosphorous present.    

On 2 December 2010, it was announced that an extremophile bacterium (GFAJ-1) can be coaxed into partially substituting arsenic for phosphorus in some of its basic chemistry under laboratory conditions.[49] Also related, on 27 June 2011, it was reported that a new E. coli bacterium was produced from an engineered DNA in which approximately 90% of its thymine was replaced with the synthetic building block 5-chlorouracil, a substance "toxic to other organisms".[50][51] Some scientists believe that these discoveries might give weight to the long-standing idea that life on other planets may have a radically different chemical makeup and may help in the search for alien life.[49][52] Jupiter's moon, Europa,[45][53][54][55][56][57] and Saturn's moon, Enceladus,[58][59] are now considered the most likely locations for extant extraterrestrial life in the solar system.

The origin of life, distinct from the evolution of life, is another ongoing field of research. Oparin and Haldane postulated that the conditions on the early Earth were conducive to the formation of organic compounds from inorganic elements and thus to the formation of many of the chemicals common to all forms of life we see today. The study of this process, known as prebiotic chemistry, has made some progress, but it is still unclear whether or not life could have formed in such a manner on Earth. The alternative theory of panspermia is that the first elements of life may have formed on another planet with even more favorable conditions (or even in interstellar space, asteroids, etc.) and then have been carried over to Earth by a variety of means. In October 2011, scientists found that the cosmic dust permeating the universe contains complex organic matter ("amorphous organic solids with a mixed aromatic-aliphatic structure") that could be created naturally, and rapidly, by stars.[60][61][62] As one of the scientists noted, "Coal and kerogen are products of life and it took a long time for them to form ... How do stars make such complicated organics under seemingly unfavorable conditions and [do] it so rapidly?"[60] Further, the scientist suggested that these compounds may have been related to the development of life on earth and said that, "If this is the case, life on Earth may have had an easier time getting started as these organics can serve as basic ingredients for life."[60

Rooting for the existence of something isn't exactly a field of science.

Allow me to help you get to the root of Astrbiology-

But there hasn't been any EXTRATERRESTRIAL BIOLOGY found. All they have to study, is TERRESTRIAL BIOLOGY ?

Astrobiology is study of life outside earth; it includes the possibility of life on other planets, possibly around other suns.

I think you need to redefine your definition of astrobiology a bit........

http://en.wikipedia.org/wiki/Astrobiology

I guess, unless you think there is biology in the astrosphere.