Why does the Catholic church not sanction the KJV translation?

First, remember that the lack of authorisation does not mean that you are not allowed to read (or enjoy!) the translation. It means that it is not officially authorised, and therefore cannot be used in liturgy, or in official church documents.

That said, there is a significant division between Catholic and Protestant bibles. They are not just different translations: they contain (to some extent) different content. For example, the Book of Esther. The entire book is presented as one in a Catholic bible, but it is presented in two parts (the Hebrew part and, separately, the Greek-only part) in Protestant bibles. (If, that is, the Greek part is given at all. It was part of the original KJV translation, but it has frequently been omitted in the intervening centuries.) This is true of various other parts of the Old Testament.

There is also the question of accuracy. The KJV is old. It was translated in 1611, and has not been updated. (Though since the late 19th century there have been various successor translations: the RV, ASV, RSV, and NRSV, along with Catholic editions of the last two. These Catholic editions are approved, though you will find that they don't include the Tudor language.) In the intervening 400 years, there have been many further discoveries of biblical manuscripts, and much work has gone on to better determine the original text and its meaning. The KJV in various places is colossally out of date.

The final point is translation philosophy. The KJV was a pretty good translation for the standards of the day, but it was not without

Historically, the Vatican has preferred the Latin translation of the bible which Jerome produced in about the year 380 A.D.

The Vatican's argument has been that this early rendering of the Greek text (extant in the time of Jerome) into Latin was a more reliable source than the Greek text itself which, due to being copied and re-copied by hand, had suffered alterations (whether deliberately or inadvertently) resulting in groups of manuscripts which disagreed one with another.

The 1989 preface to the Duoay Rheims bible states :

Sometimes the question is raised: Why translate from a translation (the Latin Vulgate) rather than from the original Greek and Hebrew? This question was also raised in the 16th century when the Douay-Rheims translators (Fr. Gregory Martin and his assistants) first published the Rheims New Testament. They gave ten reasons, ending up by stating that the Latin Vulgate “is not only better than all other Latin translations, but than the Greek text itself, in those places where they disagree.” (Preface to the Rheims New Testament, 1582). They state that the Vulgate is “more pure than the Hebrew or Greek now extant” and that “the same Latin hath bene farre better conserved from corruption.” (Preface to the Douay Old Testament, 1609).

CCWatershed.org

It is for this very reason that The Wycliffe bible was also translated from Jerome's Vulgate in 1388.

At the time it was, in fact, a very valid argument. However, men devoted their lives to gathering together as many ancient manuscripts as they could and in the sixteenth century a reliable Greek Text was produced, by such as Erasmus (1516) Stephanus (1550) Beza (1598) and Elzevir (1624).

This Greek Text acknowledged the Vulgate but also acknowledged the Greek manuscripts available, the other ancient translations of the Greek (the Syriac and Egyptian, for example) the 'Patristic Citations' (scripture quotes by such as Eusebius and Augustine) and the 'Lectionaries' (the orders of service - much like the English 'Book of Common Prayer' - which quoted scripture).

With all this amassed evidence the 'Received Text', as it came to be known, in 1624, was the most reliable version of the Greek New Testament writings in existence at the time.

But the Vatican had, secreted in its library during the 1500s (or maybe earlier), another Greek text which had not been made available to the collaters of the Received Text. This was the Codex Vaticanus. And, indeed, it was true that the Vulgate was a far more reliable source than the Greek text held in the Vatican.

The Codex Vaticanus was, indeed, a fine example of a manuscript, excellently preserved. But it was a fine example of a corrupted manuscript, an example of what had happened (and was known to have happened) in the second century - when error had crept into the early church and copyists had been inclined to alter the Greek text accordingly.

The history of the early church indicates how quickly heresies arose and how they had to be resisted by such means as the First Council of Nicaea, convened to resist Arianism.

It is noticeable that the Codex Vaticanus omits, for example, the words 'the Son of God' from Mark 1:1. 'The beginning of the Gospel of Jesus Christ, the Son of God.

Once released, around the beginning of the 20th century, it became clear that the Codex Vaticanus differed greatly from the Textus Receptus.

I believe that the issues of the Latin Vulgate and the later issue of the release of the Codex Vaticanus are the fundamental reasons for the Vatican not accepting the validity of the King James Authorised bible which is based, very firmly, on the Received Text and is demonstrably different - in many places - from the Codex Vaticanus.

John Burgon, a Textual Critic of massive achievement in his field (he personally collated 96,000 Patristic Citations in order to reinforce the validity of the Received Text) resisted, in 1881, the attempt to give disproportionate weight to the Codex Vaticanus (and its cousin the Codex Sinaiticus) in his book 'Revision Revised' :

Burgon assailed Westcott & Hort in a memorable 1881 article in the Quarterly Review, and collected his Quarterly Review articles and pamphlets into books, such as "The Revision Revised", in which he denounced Westcott and Hort for elevating "one particular manuscript,--(namely the Vatican Codex (B), which, for some unexplained reason, it is just now the fashion to regard with superstitious deference". He found their primary manuscript to be "the reverse of trustworthy."

Wiki

In the past, the Catholic church had a serious monopoly on Bible translations. Most bibles were exclusively in Latin. A language which was reserved for the higher members of society, the Scholars and Church leaders. The average working person could not read the bible for themselves. And Catholic church services were presented in Latin too.

During the reformation Era, many people began to desire to translate the bible into the "common language" of the people. Martin Luther did this in Germany, Wycliff, and tyndale in English and others too. These Bibles were all "un-Authorized" because the Catholic church was not interested in approving these these protestants to translate the bible.

During this same time period, the king of England (Henry the 8th) Decided (for seemingly petty reasons) That he was going to leave the Catholic Church, and count himself as the head of the Church of England.

The history of England's monarchy gets pretty messy here, but Henry 8 dies ~1547 And "King James 1" Comes in ~1603.

Now that they are officially separated from the Catholic church and the king of England is the head of the "Church of England", he is now the one who "authorizes" requests for bible translations.

He gives his approval and now they make the King James Bible, also known as the "Authorized" translation.

The whole point of the history is I would imagine the Catholic church doesn't really accept that bible because it was never their bible, and was translated against their wishes, under an opposing king.

Briefly, the Catholic Church doesn't accept the King James Version/Authorized Version for the same reason that it doesn't accept as authoritative any bible containing only the protocanon, or containing the deuterocanon only under the description of "Apocrypha".

Bibles fitting this description display an understanding of Sacred Scripture very different from the Catholic understanding. This makes it likely that the translation will not be in accord with Catholic teachings. Since this could result in misunderstanding of catholic teaching, the Church does not use them for liturgical functions, and does not endorse them for devotional use. They may, however, be studied as literary works, or as exercises in comparative translation.

In order for a Bible translation, or any other book, to be considered acceptable to consider "Catholic", it needs to have an imprimatur from the local bishop. The website of the United States Conference of Catholic Bishops contains a list of Bible translations approved for devotional use, as well as recommending any translation with an imprimatur.

This is to address a part of OP's question which does not yet seem addressed in the existing answers. He asks about differences between the KJV and traditional Catholic Bibles, and whether the KJV was "fundamentally changed" to fit a Protestant perspective.

The Douay-Rheims Version, as Ken Graham points out, was completed before the KJV and this was the traditional Catholic Bible against which the KJV can be compared. There were differences and it was the view of English-speaking Catholics that they were the result of errors in the KJV, and that these errors fitted a Protestant perspective, and that some, at least, were deliberate. Protestants usually took the opposite view, claiming it was the Douay-Rheims version (DRV) which had deliberate errors in it.

Thomas Ward, a seventeenth century English convert to Catholicism, published a book in 1688 called "Errata of the Protestant Bible" listing numerous differences and explaining their significance. This edition, with some additional material, was published in Dublin in 1841. It deals with "errors" in the KJV but also many in earlier versions which were corrected in the KJV (the last column in his tables shows the KJV position). It is written in the highly polemical style typical of its time.

Below are just some of these, with a summary of their significance (my attempted summary of what Ward wrote at much greater length) In each case I will put the Douay-Rheims verse first, followed by the King James. Many are very subtle.

The Mass

Genesis 14 v18

But Melchisedech the king of Salem, bringing forth bread and wine, for he was the priest of the most high God,

And Melchizedek king of Salem brought forth bread and wine: and he was the priest of the most high God.

Here the DRV shows bread and wine as intrinsic to Melchisedech's priesthood, whereas the KJV suggests the fact Melchisedech was a priest, and the fact he brought forth bread and wine are two possibly unrelated facts.

1 Corinthians 11 v27

Therefore whosoever shall eat this bread, or drink the chalice of the Lord unworthily, shall be guilty of the body and of the blood of the Lord

Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord

The difference here is that Protestants received both the bread and wine whereas Catholics generally received only bread (communion in one kind only). The different translations of this verse seem to reflect this difference in practice.

Jeremiah 11 19

And I was as a meek lamb, that is carried to be a victim: and I knew not that they had devised counsels against me, saying: Let us put wood on his bread, and cut him off from the land of the living, and let his name be remembered no more.

But I was like a lamb or an ox that is brought to the slaughter; and I knew not that they had devised devices against me, saying, Let us destroy the tree with the fruit thereof, and let us cut him off from the land of the living, that his name may be no more remembered

This verse was interpreted by Jerome as a Eucharistic prophecy of the Crucifixion in which Christ's body is referred to as "bread". The Protestant translation by referring to "fruit" rather than "bread" negates this interpretation.

Penance

Luke 3 v3

preaching the baptism of penance for the remission of sins

preaching the baptism of repentance for the remission of sins

Acts 2 v38

Peter said to them: Do penance, and be baptized every one of you in the name of Jesus Christ,

Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ

In each of these verses, one referring to the message of John the Baptist and the other to the events of the first Whitsun, the Catholic Bible has penance while the Protestant one has only repentance.

Priestly Celibacy

1 Corinthians 9 v5

Have we not power to carry about a woman, a sister, as well as the rest of the apostles

Have we not power to lead about a sister, a wife, as well as other apostles

Here St Paul is saying that as an apostle he has the right to a lady companion, but only in the Protestant Bible is it stated she could be his wife.

Mary

Luke 1 v28

And the angel being come in, said unto her: Hail, full of grace, the Lord is with thee: blessed art thou among women

And the angel came in unto her, and said, Hail, thou that art highly favoured, the Lord is with thee: blessed art thou among women

There is at least a difference in degree between being full of grace and being highly favoured.

Worship of Inanimate Objects

Psalm 99 v5 (Psalm 98 according to the Catholic reckoning)

Exalt ye the Lord our God, and adore his footstool, for it is holy

Exalt ye the LORD our God, and worship at his footstool; for he is holy.

Hebrews 11 21

By faith Jacob dying, blessed each of the sons of Joseph, and adored the top of his rod

By faith Jacob, when he was a dying, blessed both the sons of Joseph; and worshipped, leaning upon the top of his staff

The DRV refers to adoration of the footstool and the rod, whereas the KJV refers to the footstool and rod as locations, not objects, of worship.

Limbus Patrum (the Limbo of the Fathers)

Genesis 42 v38

you will bring down my gray hairs with sorrow to hell

then shall ye bring down my gray hairs with sorrow to the grave.

Here, Jacob is fretting about what will happen to him if he allows Benjamin to travel to Egypt and he does not come back. According to the DRV he expects, on death, his soul will go to hell, whereas according to the KJV he is talking about the burial of his body. There are several similar verses.

Papacy

Malachi 2 v7

For the lips of the priest shall keep knowledge, and they shall seek the law at his mouth: because he is the angel of the Lord of hosts.

For the priest's lips should keep knowledge, and they should seek the law at his mouth: for he is the messenger of the LORD of hosts

An interpretation of this verse is that it is a prophecy of the Papacy. The DRV says what "shall" happen, a definite statement about the future, the KJV says what "should" happen but with no guarantee that it will.

Royal Supremacy

1 Peter 2 13

Be ye subject therefore to every human creature for God's sake: whether it be to the king as excelling; Or to governors ...

Submit yourselves to every ordinance of man for the Lord's sake: whether it be to the king, as supreme; Or unto governors ...

Here the DRV describes the king as "excelling", the KJV asserts that he is "supreme". Not all Protestants believe in Royal Supremacy, but the Church of England does, and King James certainly did (as indeed did several Catholic monarchs). The Catholic Church regarded the Pope as supreme.

Priests

1 Timothy 4 14

Neglect not the grace that is in thee, which was given thee by prophesy, with imposition of the hands of the priesthood.

Neglect not the gift that is in thee, which was given thee by prophecy, with the laying on of the hands of the presbytery

Acts 14 v23

And when they had ordained to them priests in every church, and had prayed with fasting, they commended them to the Lord, in whom they believed.

And when they had ordained them elders in every church, and had prayed with fasting, they commended them to the Lord, on whom they believed.

The DRV refers to Christian priests being ordained by Paul and Barnabas whereas the KJV calls them elders. The DRV refers specifically to ordination conferring grace, which the KJV terms a gift, which may reflect a more sacramental understanding of ordination in the Catholic Church. There are several other verses where the DRV says "priest" and the KJV has "elder". The KJV also has "overseer" in some of the places where the DRV has "bishop", although the KJV does refer to bishops (e.g. 1 Timothy 3 v1).

Salvation by Faith

Luke 18 42

And Jesus said to him: Receive thy sight: thy faith hath made thee whole

And Jesus said unto him, Receive thy sight: thy faith hath saved thee

The DRV has Jesus talking of physical healing whereas the KJV suggests salvation, as a result of faith.

Summary:

The King James Version differed in numerous, often very subtle, ways from the DRV on points of disputed doctrine.

The circumstances of its translation, and the description of the Pope as "that man of sin" in the Epistle Dedicatory (translators letter to James) hardly endeared it to the Catholic Church. Also there was already a Catholic translation in the DRV so the KJV would, in any case, have been superfluous. But beyond all these reasons there were genuine doctrinal differences between the two.

A brief history of events leading up to the publication of the King James Authorised version of the Bible may help to explain why the Catholic Church does not sanction this translation.

Mary Queen of Scots gave birth to her son James in 1566 in Scotland. In June 1567 the Protestant lords rebelled against their queen. They arrested and imprisoned Mary in Loch Leven Castle, where she was forced to abdicate the throne of Scotland. James was only a year old when he became James VI, King of Scotland, in 1567. In spite of his mother’s Catholic faith, James was brought up in the Protestant religion. He was educated by men who had empathy for the Presbyterian Church. It was not until 1603, upon the death of Queen Elizabeth I, that the kingdoms of Scotland and England were united and James became King James I of England, the first of the Stuart line.

King James often wrote against the power of the pope and against Catholicism’s meddling in affairs of state. In his opposition to the pope’s power, James promoted the divine right of kings—the idea that kings are accountable to God and no one else. In 1605, a group of Catholics attempted to assassinate James and his wife and son and to blow up Parliament; however, the Gunpowder Plot was foiled. That incident is remembered today as Guy Fawkes Day.

The Puritans and Scottish Presbyterians wanted a new Bible that would get as far away as possible from the structure of the Bishops’ Bible of the Anglican Church. The Bishops' Bible was an English translation of the Bible produced under the authority of the Church of England in 1568, whose bishops were offended by the Geneva Bible, the notes of which were decidedly Calvinistic in tone. The Great Bible was considered deficient because it was translated from the Latin Vulgate, and so a new translation was authorized by the Anglican bishops and came to be known as the Bishops’ Bible.

The idea of a new translation of the Bible was first proposed at a religious conference in Aberdour, Fife. King James was in favour of a new translation. He didn’t care for Tyndale’s translation of Matthew 16:18, which said Christ would build His “congregation” on Peter (James much preferred “church” from ekklesia). The only other alternative at the time was the 1560s Geneva Bible, but King James objected to a “treasonable annotation” on Matthew 2:20 that suggested that kings are tyrants.

King James Version - Translation method: “The King James translation was done by 47 scholars, all of whom were members of the Church of England. In common with most other translations of the period, the New Testament was translated from the Textus Receptus (Received Text) series of the Greek texts. The Old Testament was translated from the Masoretic Hebrew text, while the Apocrypha was translated from the Greek Septuagint (LXX), except for 2 Esdras, which was translated from the Latin Vulgate. In 1769, the Oxford edition, which excluded the Apocrypha, became the standard text and is the text which is reproduced almost unchanged in most current printings.” Source: What is the King James Version (KJV)?

Reason 1: King James VI of Scotland and 1 of England opposed the power of the Pope and claimed the divine right of Kings

Reason 2: The 1769 Oxford edition of the King James Authorised Version excluded the Apocrypha

Reason 3: King James VI of Scotland and 1 of England and the 47 translators were Protestants

There may be other reasons, but those are the main ones I found when doing research into this subject a few years ago. My sources were taken from a wide variety of historical and theological articles.