Reform movements usually argue that a church has gone wrong. The Latter-day Saint claim is stronger and different in kind: that after the death of the New Testament apostles the authority to act for God was withdrawn from the earth altogether, and that no institution retained it. This is what the movement means by the Great Apostasy, and it is not a claim about corruption, doctrine or morals in the first instance. It is a claim about priesthood keys.
The consequence is immediate and unavoidable. If no valid authority existed, then no baptism performed between the second century and 1829 was valid, no ordination conferred anything, and the sacraments of every intervening church were sincere but empty. That is why Latter-day Saint practice rebaptises every convert, including a lifelong Catholic, an Orthodox priest or a Baptist minister, and it is the single position that other Christian bodies find hardest to accommodate. The Catholic Church, which recognises the baptisms of most Protestant denominations, declined in 2001 to recognise Latter-day Saint baptism, and most Protestant bodies take the same view.
Latter-day Saints read the New Testament itself as anticipating the apostasy, citing Paul's warning to the Thessalonians of a falling away, Amos on a famine of hearing the word, and Acts on the restitution of all things. Historians outside the movement do not find a moment at which authority can be said to have lapsed, and treat the doctrine as a nineteenth century reading of the early church rather than as a finding about it. The disagreement is genuine, it is old, and neither side has moved.