When the great apostasy begins — and I believe this will happen during the Year of Faith — most Catholics will leave the Church. They will no longer call themselves Catholic. They will no longer attend Mass, even on Christmas and Easter. They will no longer financially support their (former) parish.
“The church will become small and will have to start afresh more or less from the beginning. She will no longer be able to inhabit many of the edifices she built in prosperity. As the number of her adherents diminishes … she will lose many of her social privileges.”
Cardinal Ratzinger (1969), republished in Faith and the Future (2009)
Now, to be fair, Cardinal Ratzinger/Pope Benedict XVI was not talking about the great apostasy specifically. He was talking about the possibility (not a prediction by him) that the Church might need to become smaller in order to become holier. But I see that his words are true, and that they apply to the great apostasy.
Why do most Catholics leave the Church at that time? It is because they already left the Church long before that time, in their hearts and minds. Most Catholics do not believe what the Magisterium teaches, do not know what the Magisterium teaches, do not want to know what the Magisterium teaches. They do not acknowledge that the Church has the role of teaching them with authority on matters of faith and morals.
Most Catholics are in a state of at least material heresy; many in a state of formal heresy.
During the Year of Faith, the new Pope will require the faithful to believe and practice what the Church teaches in order to receive the Sacraments. Most Catholics will be outraged that Catholics would be required to believe what the Catholic Church teaches, and they will depart from the true Faith.