The widespread heresy is the claim that the Bible is only inerrant on matters of faith and morals. The dogma is that the Bible is inerrant on every subject about which it makes an assertion, including history, geography, and physical sciences. This teaching is a matter of faith. Catholic Christians ought to believe, regardless of how many apparent errors there may be, as an act of supernatural faith. And yet the heresy is very widespread.
1. Secular Influence
One reason for the prevalence of this heresy is the teaching of sinful secular society that gives an excess of credibility to whatever science teaches. And when science changes its view, as often happens when a field of knowledge advances, no one seems to notice that the previous view, accepted as if it were infallible dogma, has now changed.
For example: In the 1920’s, scientists believed the universe was infinite and always existed, in contradiction to Catholic dogma. Then, in the 1930’s, Fr. George Lemaitre discovered the big bang theory, which concludes that the universe is finite and had a starting point. Science was wrong, and the faith was right. But how many persons in the 20’s held to the teachings of faith over that of science?
Most Catholics are thoroughly secularized. They believe nearly everything taught by secular society. So when an assertion in the Bible seems to conflict with what science or history teaches, they are heavily biased against the Bible.
Trust the Bible.
2. Doubting the Power of God
Do you believe that God created the whole universe out of nothing? Do you believe that He creates each soul out of nothing? Do you believe that Jesus performed miracles, including healings and raising from the dead? Do you believe that Jesus himself died, rose, and ascended to Heaven?
Then why is it so hard to believe that God could write a book without error? The prevalence of this heresy on Biblical inerrancy shows a lack of faith.
Have faith in God.
3. Misinterpretation
Often a passage seems to be in error due to misinterpretation. Some assertions are figurative, and others are literal. As a set of events is described, a long time might pass between one verse and the very next verse. Different names might be used to describe the same person. And the things of nature are often described by appearances, rather than by the categories used today.
If a passage appears to be asserting a falsehood, seek a different interpretation. The passages that say the earth is firm, not to be moved (Ps 104:5), were at one time interpreted to mean that the sun revolves around the earth. And the solution to this problem is that the verse is to be understood as figurative, not literal.
Consider other interpretations.
4. Exalting reason over faith.
Our religion is based on faith and reason. But of the two, faith should have the higher place. So when there is a conflict, we should believe even things that reason cannot explain.
Choose faith over reason.
Vatican I: “Hence all faithful Christians are forbidden to defend as the legitimate conclusions of science those opinions which are known to be contrary to the doctrine of faith, particularly if they have been condemned by the Church”
by
Ronald L. Conte Jr.
Roman Catholic theologian and translator of the Catholic Public Domain Version of the Bible.
Please take a look at this list of my books and booklets, and see if any topic interests you.
the reproach of Christ 
What are some of the reasons for this lack of faith in the Scriptures? Off the top of my head:
1) embarrassment of miracles
2) secular, skeptical academia; from what I hear, even in Catholic colleges and worse, seminaries, students learn that the Bible has errors, we don’t know who wrote the Gospels, etc.
3) History, Discovery Channel, etc. shows which are extremely conspiratorial against the Bible and Christianity (i.e. Catholics formed by pop culture Christianity instead of the Church)
4) lack of preaching and teaching of Scripture at the parish level
5) the notoriously misleading, confusing, and skeptical footnotes of the NAB, which the majority of American Catholics own and use
6) the perceived errors of the Bible, most of all alleged in Genesis
7) the perceived incompatibility of faith and science
8) elevation of science, and unlimited acceptance of evolution not only as a biological science but an overarching philosophy affecting every aspect of life (morality must evolve, marriage must evolve, etc.); “evolve” being a code-word for “move away from Catholic teaching”
9) lack of regular prayer
10) lack of condemnation from the Church concerning erroneous Scripture scholarship; some early 20th century PBC-style statements seem to be needed again
11) lack of “follow up” regarding Vatican documents which teach things directly revealed in Scripture; case in point, Pope Pius XII’s call to have a balanced debate about evolution has been taken over almost completely by those advocating for unguided evolution, to the point where many theologians now try to claim polygenism is compatible with the faith
12) ultimately, a glaring lack of “ownership” by the Church to correct these errors over the last 50-60 years; thankfully, some faithful Catholic Scripture scholars have picked up the slack, but they are swimming against the tide.
Good. I will say that Biblical scholars have largely abandoned faith in the bible. They literally say “The Bible should be interpreted without faith.” Those exact words. It is the embarrassment of Christ. They don’t want faith, they want to be like secular scholars, who rely only on reason and research.
There are some very good, popular Catholic Scripture scholars today, at least here in America. The contributors to the website “The Sacred Page” are pretty good, and I have read several of their books.
To add to the list above, “relativism” is another reason. Many Catholics think, “every religion has their own sacred texts, so why should ours be held in higher esteem than theirs?”
From my informal assessment of blog posts, comments on Catholic Answers Forums, etc., it seem that many Catholics actually grasp Biblical passages which are settled doctrines. For instance, it seems most of them can defend things like listing the Biblical justification for the sacraments, can link OT prefigurements to our Blessed Mother, etc. But in what may be called the “speculative” realm is where it becomes problematic, with many of them denying that we know who wrote the Gospels, advocating for polygenism, insisting that events like the Massacre of the Holy Innocents did not occur, denying any actual flood ever occurred, saying that Adam’s name is not important, picking apart the Pentateuch as legendary and not historical, accusing Luke of historical inaccuracies, and in general advocating secular skeptical scholarship over perennial traditional teaching of the Church.