There are four major reasons to believe the New Testament is Eurocentric: (1) the original manuscripts were written in Greek, (2) the New Testament events transpired within European dominated civilization, (3) it prioritizes the conversion of north Mediterranean ethnic groups, and (4) a huge portion of the New Testament was specifically written to European audiences. God might have intended this shift to represent a broader change in the world's religious center.
Firstly, the New Testament was written in the European language of Greek. This contrasts with the Old Testament which was written in the Near Eastern Hebrew language. The New Testament was written by Jews so there is no reason the documents needed to be written in Greek.
Secondly, the events of the New Testament occurred entirely within a European dominated civilization. Prior to the first century, Alexander the Great had conquered the Near East and shifted the world's political and cultural center to Europe. He exported the Greek language and culture. Christ lived and died within the context of a European civilization. There are no significant events recorded in the New Testament that occur outside the European dominated society of the first-century Roman world.
Thirdly, the New Testament prioritizes the conversion of European and Anatolian ethnic groups over other regions and peoples. The Acts of the Apostles is the only book of history contained in the New Testament and it records mission work that occurred towards and into Europe. Acts also records a specific mandate God gave the apostle Paul to leave Asia and preach in Europe (Acts 16). Paul evangelized in Greece and Italy, and planned a trip into Spain, but he never went to Africa or East Asia. The New Testament never specifically mentions an evangelization into Africa or East Asia (Acts 8 does not record evangelization in Africa).
Fourthly, all of the New Testament epistles addressed to congregations, with the exception of Hebrews, were written to churches north west of Jerusalem. Eight of them (Romans, 1 & 2 Corinthians, 1 & 2 Thessalonians, Ephesians, Philippians, Colossians) were written to churches in Europe. Among these eight epistles (1 Thessalonians) is probably the first document authored in the New Testament. Revelations, John's book of prophesy, was addressed to the "seven churches of Asia" which were located in the Greek influenced Western region of Anatolia. There are no New Testament books specifically written to an African or East Asian audience.