I quote at length from 'The Garden Tomb: Was Jesus Buried Here?' by Gabriel Barkay (pp. 27-36 of this PDF booklet by the Biblical Archaeology Society, The Burial of Jesus).
A long and extremely bitter dispute concerning the authenticity of the site followed Gordon’s identification of the hill as Golgotha and the consequent identification of the cave in its western escarpment as Jesus’ tomb. The authenticity of the tomb was supported mainly by Protestants. It was attacked mainly by Catholics, who held to the traditional identification of Jesus’ tomb within the Church of the Holy Sepulchre. The dispute was conducted in scores of articles in a number of journals. Most of these articles have a theological and apologetic, rather than a scientific bent. None concerning the cave, nor any useful analysis of the archaeology of the site.
In 1904, Karl Beckholt, who was serving as Danish consul in Jerusalem and as warden of the Garden Tomb, conducted a small excavation in the yard of the Garden Tomb. He found some objects, which were published 20 years later by a Jerusalem scholar and Anglican clergyman named James Edward Hanauer. This 1924 publication renewed the bitter dispute about the location of the authentic tomb of Jesus. The opposing positions were summarized in a sharply worded article written from the Catholic point of view by Louis-Hugues Vincent, one of the Dominican scholars at the École Biblique. Father Vincent, a leading scholar on the archaeology and history of Jerusalem, defended the position that the Garden Tomb cave was of the Byzantine period. He entitled his article “The Garden Tomb—History of a Myth.”
In 1955, the Garden Tomb Association sponsored a small excavation in the garden area. Unfortunately, nothing is known about this dig; it was never published.
The dispute over the authenticity of the Garden Tomb was again summarized in 1975 in a book entitled The Search for the Authentic Tomb of Jesus by W. S. McBirnie, who advocates the Garden Tomb’s authenticity. McBirnie’s book, however, is not based on any archaeological information, nor is the author knowledgeable about the history of the area in ancient times.
Thus, almost all published articles dealing with the Garden Tomb from its discovery through 1975 have been polemical, written to prove certain theological presuppositions. Except for the first article by Conrad Schick, who reported the actual discovery of the cave, there has been no objective, factual and archaeological discussion of the Garden Tomb.
To understand why this is so, we need to look at the historical situation in the late 19th century. The growing western interest in the ancient Near East, the Holy Land and Jerusalem brought hordes of visitors and pilgrims who took a new and often critical approach to the traditional holy sites. More and more Protestants came to Jerusalem, and they began to question the authenticity of the holy sepulcher. Located as it is in the midst of a densely built-up area of the Old City, the Church of the Holy Sepulchre did not seem to the Protestants to be a suitable place, outside the city, as Jewish law required, where Jewish dead would have been buried in the early Roman period. The traditional site of the sepulcher within the church was in those days dark, dismal and frequently filthy. It was crowded with priests, monks and pilgrims, mainly from Eastern countries, who often bickered with each other over rights to light candles and to hold ceremonies in various parts of the church. The Protestant newcomers did not feel at home here and could not imagine that this site could be the authentic burial place of Jesus. In this frame of mind, they welcomed any suggestion locating Jesus’ tomb in a place that would better fit the tastes of Protestant Westerners, especially because the Protestants were wholly without any proprietary share in the Church of the Holy Sepulchre, which was divided among the Greek Orthodox, Roman Catholic, Armenian and Coptic Churches.
The earliest recorded tradition about Jesus’ burial in the Holy Sepulchre is about three centuries after the Crucifixion. The New Testament itself gives no clue whatever as to the location of Golgotha and the tomb of Jesus. The name Golgotha has not been preserved in any form in any written source in antiquity, either Jewish or non-Jewish. It is not attested in geographical names in or around Jerusalem. This was enough to lead many wishful Protestants to reject the authenticity of the Church of the Holy Sepulchre.
On the other hand, there was never any sound scientific basis for locating the tomb of Jesus in the area of the Garden Tomb. The identification of the Garden Tomb as the tomb of Jesus thus reflects the psychology and atmosphere of late 19th-century Jerusalem, rather than any new evidence—scientific, textual or archaeological.