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Why can there be only one Church?
Just as there is only one Christ, there can be only one Body of Christ, only one Bride of Christ, and therefore only one Church of Jesus Christ. He is the Head, the Church is the Body. Together they form the "whole Christ" (St. Augustine). Just as the body has many members yet is one, so too the one Church consists of and is made up of many particular churches (dioceses).
Jesus built his Church, which subsists in the Catholic Church, on the foundation of the apostles. This foundation supports her to this day. The faith of the apostles was handed down from generation to generation under the leadership of the Pope, the Petrine ministry, "which presides in charity" (St. Ignatius of Antioch). The sacraments, too, which Jesus entrusted to the apostolic college, still work with their original power. (YOUCAT question 129)
Dig Deeper: CCC section (811-816) and other references here.