Just as individuals can separate themselves from the Church by heresy or schism, so the Church can separate individuals from her visible body by her own authority through sentence of perfect excommunication.
It must be that only those professing the true faith can reasonably be considered Catholic. Otherwise, we would be in the position of stating that those who publicly reject the rule of faith nonetheless share in the 'profession of the same faith' with those who do give their submission.
There is a threefold authority in the Church – that of sanctifying, teaching, and governing. Members of the Church must be subject to this threefold authority of Jesus Christ in order to become, and remain, members of the Catholic Church.
'[The Roman Catechism] contains all that is needful for the instruction of the faithful; and it is written with such order, clearness and majesty that through it we seem to hear holy Mother the Church herself, taught by the Holy Ghost, speaking to us.'