A summary of the different fields relating to the "myth theory":

Christ myth theory

The one referred to in this thread.

Historicity of Jesus

The historicity of Jesus concerns whether Jesus of Nazareth existed as a historical figure, whether the episodes portrayed in the gospels can be confirmed as historical events as opposed to myth, legend, or fiction, and the weighing of the evidence relating to his life.

Historical reliability of the Gospels

The historical reliability of the Gospels refers to the reliability and historic character of the four New Testament gospels as historical documents. Some scholars state that little in the four canonical gospels is considered to be historically reliable

Historical Jesus

The term "historical Jesus" refers to attempts to "reconstruct the life and teachings of Jesus of Nazareth by critical historical methods", in "contrast to Christological definitions ('the dogmatic Christ') and other Christian accounts of Jesus ('the Christ of faith')".[3] It also considers the historical and cultural context in which Jesus lived.

The Dogmatic Christ

In the Roman Catholic Church, a dogma is an article of faith revealed by God, which the magisterium of the Church presents as necessary to be believed if one freely chooses to be a Catholic.[a] For example, Christian dogma states that the resurrection of Jesus Christ is the basic truth from which salvation and life is derived for Christians. Dogmas regulate the language, how the truth of the resurrection is to be believed and communicated.

Some points I find particularly interesting:

Theological bias

• John Meier, a Catholic priest and a professor of theology at University of Notre Dame, has stated "... I think a lot of the confusion comes from the fact that people claim they are doing a quest for the historical Jesus when de facto they’re doing theology, albeit a theology that is indeed historically informed ..." Meier also wrote that in the past the quest for the historical Jesus has often been motivated more by a desire to produce an alternate Christology than a true historical search.

• The British Methodist scholar Clive Marsh has stated that the construction of the portraits of Jesus as part of various quests have often been driven by "specific agendas" and that historical components of the relevant biblical texts are often interpreted to fit specific goals. Marsh lists theological agendas that aim to confirm the divinity of Jesus, anti-ecclesiastical agendas that aim to discredit Christianity and political agendas that aim to interpret the teachings of Jesus with the hope of causing social change.

• The New Testament scholar Nicholas Perrin has argued that since most biblical scholars are Christians, a certain bias is inevitable, but he does not see this as a major problem.

Lack of methodological soundness

• "(...) with very few exceptions, the historians attempting to reconstruct a biography of the man apart from the mere facts of his existence and crucifixion have not followed sound historical practices. He has stated that there is an unhealthy reliance on consensus, for propositions, which should otherwise be based on primary sources, or rigorous interpretation. He also identifies a peculiar downward dating creep, and holds that some of the criteria being used are faulty. He says that the overwhelming majority of biblical scholars are employed in institutions whose roots are in religious beliefs. Because of this, more than any other group in present day academia, biblical historians are under immense pressure to theologize their historical work. It is only through considerable individual heroism, that many biblical historians have managed to maintain the scholarly integrity of their work."

• "...the 'historical Jesus' is properly speaking a nineteenth- and twentieth-century construction using the data provided by the Synoptic tradition, not Jesus back then and not a figure in history."

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Some articles:

Did historical Jesus really exist? The evidence just doesn’t add up.

Writer finds no mention of Christ in 126 historical texts and says he was a 'mythical character'

Why a historical Jesus never existed

Did the historical Jesus exist? A growing number of scholars don’t think so

Historical Jesus? Not So Fast.