Though including a reflection related to YEC, this goes beyond and deals with Biblical Inerrancy in general.
Trent Horn* has a thing or two to say:
However, the genealogies in the Bible cannot be used to date the age of the universe because they were not meant to be exact chronicles of history. In some cases generations were omitted in order to make a symbolic point. In other cases the ages themselves may be symbolic and not literal [the chapters not accessible in preview]. The genealogies in Scripture were primarily focused (sic!) on showing how different people were related to each other, not how long ago they lived.
In contrast with Ussher's exactness, the Catholic Church does not teach that either the Earth or the physical universe is of any particular age. The First Vatican Council only requires Catholics to believe that "the world and all things which are contained in it, both spiritual and material, as regards their whole substance, have been produced by God from nothing.
(From kindle edition, no pagination)
Not quite, Trent Horn, not quite.
First of all, the Catholic Church has per its Latin and Byzantine Rites probably at least two official - diverging - dates for how old Earth was when Christ was born.
In the Rite of St Pius V, the Christmas proclamation states "in the year five thousand one hundred ninety nine after the beginning when God created Heaven and Earth". The Byzantine rite, whether in that context or other, whether liturgically or just historically, whether among Uniates or just among Schismatics, says Earth was in fact 5508 years old at the first Christmas.
Only in Modern Rite is this replaced with "unknown ages". This does not even happen at Liturgic Deformation by "Paul VI", it happens even later, in 1994.
Second, you get Biblical usage somewhat wrong.
Yes, in the genealogy of St Matthew, the husband, son and grandson of Athaliah (the one bad woman who was too bad to mention in it) are omitted. The reason can be termed "symbolic", but the reason is not simply making it 14 in order to concur with the Hebrew gematria of David. That would have been cheating. It does become, after omission, 14 generations from king David to Babylonian captivity, but there is another reason for the omission. These generations are passed over by damnatio memoriae.
Precisely as in Hebrew Bible the generations go Sem, Arphaxad, Sale, while in LXX they go Sem, Arphaxad, Kainan, Sale. Hebrews were familiar with the convention of omitting bad people in genealogies. Greeks weren't. Hebrew and Greek LXX version of genealogy in Genesis 11 differ like Matthew and Luke as regards omitting or including sinners (said three generations omitted by St Matthew, said Kainan included by St Luke).
And if an age seems for any reason symbolic (like 365 years for Henoch and 777 years for Lamech, in each case the Sethite, not the Cainite ones), this in no way precludes there is a literal information. God can have arranged events (including lifespans) to concur with symbolic reasons. Indeed, since date for Christmas depends on calculated date for Annunciation, and Annunciation date on Good Friday date, the dating of Christmas in Patristics depends on counting on God regularly doing so in the lives of holy people, namely letting death date coincide with either birth or conception date.
Third, you cited what the Holy Council of the Vatican had to say about Creation (in contrast with Atheism, Pantheism etc), but not what it had to say on authority of the Bible or what Trent had to say on it.
Since your name is Trent, that is somewhat of a drastic oversight.
Anathema 1:5 is cited correctly:
If anyone does not confess that the world and all things which are contained in it, both spiritual and material, were produced, according to their whole substance, out of nothing by God; or holds that God did not create by his will free from all necessity, but as necessarily as he necessarily loves himself; or denies that the world was created for the glory of God: let him be anathema.
But how about 2:4?
If anyone does not receive as sacred and canonical the complete books of Sacred Scripture with all their parts, as the holy Council of Trent listed them, or denies that they were divinely inspired : let him be anathema.
Or 4:2, 4:3?
If anyone says that human studies are to be treated with such a degree of liberty that their assertions may be maintained as true even when they are opposed to divine revelation, and that they may not be forbidden by the Church: let him be anathema.
If anyone says that it is possible that at some time, given the advancement of knowledge, a sense may be assigned to the dogmas propounded by the Church which is different from that which the Church has understood and understands: let him be anathema.
Or before anathemas, in the explanatory part:
Now this supernatural revelation, according to the belief of the universal Church, as declared by the sacred Council of Trent, is contained in written books and unwritten traditions, which were received by the apostles from the lips of Christ himself, or came to the apostles by the dictation of the Holy Spirit, and were passed on as it were from hand to hand until they reached us .
The complete books of the old and the new Testament with all their parts, as they are listed in the decree of the said Council and as they are found in the old Latin Vulgate edition, are to be received as sacred and canonical.
These books the Church holds to be sacred and canonical not because she subsequently approved them by her authority after they had been composed by unaided human skill, nor simply because they contain revelation without error, but because, being written under the inspiration of the Holy Spirit, they have God as their author, and were as such committed to the Church.
Or Trent, Session IV - Celebrated on the eighth day of April, 1546 under Pope Paul III:
Following, then, the examples of the orthodox Fathers, it receives and venerates with a feeling of piety and reverence all the books both of the Old and New Testaments, since one God is the author of both; also the traditions, whether they relate to faith or to morals, as having been dictated either orally by Christ or by the Holy Ghost, and preserved in the Catholic Church in unbroken succession.
It has thought it proper, moreover, to insert in this decree a list of the sacred books, lest a doubt might arise in the mind of someone as to which are the books received by this council.
[follows here a list]
If anyone does not accept as sacred and canonical the aforesaid books in their entirety and with all their parts, as they have been accustomed to be read in the Catholic Church and as they are contained in the old Latin Vulgate Edition, and knowingly and deliberately rejects the aforesaid traditions, let him be anathema.
Will there be a second edition without this blunder?
Hans Georg Lundahl
* Hard Sayings: A Catholic Approach to Answering Bible Difficulties Hardcover – June 30, 2016
by Trent Horn (Author)