This question illustrates the fundamental differences between the SSPX and the Conciliar “traditionalists” or conservatives. These latter are often seen defending both the traditional Roman Mass and the “new” Catechism but not openly attacking either the Novus Ordo Missae or Vatican II.
The SSPX on the other hand defends the traditional catechisms and therefore the traditional Mass, and so attacks the Novus Ordo Missae, Vatican II and the “new” Catechism, all of which more or less undermine our unchangeable Catholic faith.
Conservatives defend the Catechism of the Catholic Church for its re-affirmation of teachings silenced or denied by out rightly modernist catechisms; the Society rejects it though because it is an attempt to formalize and propagate the teachings of Vatican II. Pope John Paul II agrees with this:
The Catechism was also indispensable (i.e., as well as the 1983 Code of Canon Law), in order that all the richness of the teaching of the Church following the Second Vatican Council could be preserved in a new synthesis and be given a new direction." (Pope John Paul II, Crossing the Threshold of Hope, London, Jonathen Cape, 1994, p. 164)
One need but consider the 806 citations from Vatican II, a number which amounts on average to one citation every three-and-a-half paragraphs throughout the 2,865 paragraphs of the Catechism.
In particular, the novelties of Vatican II appear in the following paragraphs:
Now, just as he who denies but one article of Faith loses the Faith [principle 7], so a teacher who errs on one point alone proves himself fallible, and, renders all he teaches questionable.
Just as the Second Vatican Council is not an authority to quote even where it propounds Catholic teaching (it does not do so infallibly and clearly), so this Catechism is not an authority of Catholic belief because of the modern deviations which it encompasses. Hence, those who defend this Catechism are supporting the innovations of Vatican II.
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