The lack of logic to the KJV-Only position is already well answered by others.
More importantly the Scriptures are our only authority in matters of our beliefs and since the KJV-Only belief cannot be substantiated from Scripture then KJV-Only-ism actually undermines the Protestant idea that the Word of God is our sole authority in matters of faith and the practice of our faith.
Nor is it enough for followers of KJV-Only-ism to try to show that the KJV is better than other versions... that would be a dishonest ruse on their part seeing it is not the point at all, because it is not their main belief.
They must show the KJV is without error.
There is a truly excellent series of short articles on this subject. The argument that the translators of the KJV were not themselves KJV-Only-ers, as proved in their introductory Preface to the 1611 KJV, is found here:-
https://dbts.edu/2012/04/25/is-only-the-king-james-version-the-word-of-god/
The KJV translators themselves write in the Preface to the 1611 version:-
...we do not deny, nay [on the contrary], we affirm and avow, that the very meanest [worst] translation of the Bible in English set forth by men of our profession…containeth the word of God, nay, is the word of God: as the King’s speech which he uttered in Parliament, being translated into French, Dutch, Italian, and Latin, is still the King’s speech, though it be not interpreted by every translator with the like grace, nor peradventure so fitly for phrase, nor so expressly for sense, every where.…A man may be counted a virtuous man, though he have made many slips in his life, (else there were none virtuous, for in many things we offend all) also a comely man and lovely, though he have some warts upon his hand, yea, not only freckles upon his face, but also scars. No cause therefore why the word translated should be denied to be the word, or forbidden to be current, notwithstanding that some imperfections and blemishes may be noted in the setting forth of it.
The other articles are chained and can be reached from the article linked above.
The full text of the Preface to the 1611 KJV, written by the translators/editors, and containing much that wholeheartedly disagrees with the KJV-Only belief can be found here:-
http://www.bible-researcher.com/kjvpref.html
Examples of error or imperfection in the KJV
In the rest of this post I want to add some examples where the KJV is wrong or contains a wrong translation or not an optimal translation. It may be it is wrong because of some error in the text of the original language, or it may be a translation error.
Nomatter how the error arose, if the KJV is itself inspired it ought to contain no errors at all.
(Please note all I write is secondhand: I have no Hebrew or Greek.)
Psalm 145
The Hebrew alphabet contains 22 letters.
Psalm 145 contains one verse for every letter of the Hebrew Alphabet. The first letter of each verse/sentence is in alphabetical order, starting with Aleph. Unfortunately one verse is missing, there are only 21 verses. A verse is missing, which should be between verses 13 and 14.
It is not the fault of the KJV translators that there are only 21 verses, the verse was lost in the original language. But the point is, if the Word of God is preserved by one translation, and that translation in English is the KJV, then the KJV ought to have put the verse back in, even the correct verse, between verses 13 and 14. The only defence to this is that in the original deliberately missed out a verse, which seems a very weak argument.
Isaiah 30:33
It may be that the KJV and all other Bible translations get this wrong and it should read something like:
For Tophet is ordained of old; yea, for Molech it is prepared; he has made it deep and large: the pile thereof is fire and much wood; the breath of the LORD, like a stream of brimstone, doth kindle it
The Hebrew word "melek" can either be translated "Molech" or "king", Molech means "king", just as Baal means "lord". And Tophet in the valley of Gehennom at Jerusalem is that place where babies were sacrificed to Molech.
So the verse may be talking about hell, in a very similar way to Matthew 25:41, i.e. the "everlasting fire, prepared for the devil and his angels".
Jeremiah 29:10
For thus says the Lord: When seventy years are completed for Babylon, I will visit you, and I will fulfil to you my promise and bring you back to this place. (Jeremiah 29:10, ESV)
Many modern bible translations have this rendering; the KJV does not & neither do the NKJV nor the New World Translation. They render it “when seventy years are completed at Babylon”. This is obviously quite a big difference. It should be noted, though, that even two versions of the JW New World Translation have changed it from “at Babylon” to “for Babylon”: the Swedish NWT, revised in 2003, and the Danish NWT. (http://kristenfrihet.se/vtsvar/vtsvar1.pdf page 5)
Of the Hebrew preposition translated “at” here in the KJV modern authorities on Hebrew agree that it means “to”, “for”, “with reference to”. They point out that it may also be used in a local or spatial sense (“in”, “at”), but only in certain adverbial expressions, and in any case not at Jeremiah 29:10, where the meaning is “for Babylon”.
The Swedish Hebraist Dr. Seth Erlandsson states that, “The spatial sense is impossible at Jer. 29:10”. Other Hebraists agree, including Professor Ernst Jenni, the leading authority on the Hebrew prepositions. His work on this preposition alone covers 350 pages! (http://kristenfrihet.se/vtsvar/vtsvar1.pdf page 5)
The idea is that the 70 years relate to the supremacy of Babylon as a super power not to the years of captivity.
Jeremiah 39:3
And all the princes of the king of Babylon came in, and sat in the middle gate, even Nergalsharezer, Samgarnebo, Sarsechim, Rabsaris, Nergalsharezer, Rabmag, with all the residue of the princes of the king of Babylon. (KJV)
In June 2007 the Nebo-Sarsekim Tablet was translated in the British Museum by Michael Jursa. See https://archive.archaeology.org/0801/topten/cuneiform.html
It is more than reasonable to suppose that the KJV has made an error of the names "Samgarnebo, Sarsechim": it should be translated "Samgar, Nebo-Sarsechim".
Also the KJV implies that "Rabsaris" and "Rabmag" are names of officials whereas "Rabsaris" means "Chief of the Eunuchs" and "Rabmag" (I think) means "Chief of the Wise Men". (The sequence is suggestive that "Samgar" is also a title.)
Jeremiah 52:31
And it came to pass in the seven and thirtieth year of the captivity of Jehoiachin king of Judah, in the twelfth month, in the five and twentieth day of the month, that Evilmerodach king of Babylon in the first year of his reign lifted up the head of Jehoiachin king of Judah, and brought him forth out of prison (KJV).
In the year that Evil-merodach became king of Babylonia, he showed kindness to King Jehoiachin of Judah by releasing him from prison. This happened on the twenty-fifth day of the twelfth month of the thirty-seventh year after Jehoiachin had been taken away as a prisoner. (GNB, Good News Bible)
This is a great verse to compare the different English translations using Biblehub because so many versions which I often hear disparaged/belittled, such as the GNB, get it right and several highly-praised translations, including the KJV, get it wrong.
The first year of the kings of Babylon is not the same year as the year in which they became king. The year a Babylonian king started to reign was his "accession year". The technical language for this seems to be used in Jeremiah 52:31 and should be translated "in the year of his becoming king", or something similar: it must not be translated "in the first year".
Explanation: The Babylonians, just like other kingdoms at the time, added one to the year of the king's reign on New Year's Day each year. Let us use January 1st as New Year's Day. Suppose a king ascends the throne on January the 5th: then according to the Babylonian Accession Year method the time from January 5th to December 31st is his "Year of Becoming King" or his "Accession Year", and the next year, starting 1st Jan, is his First Year. Similarly, if a king becomes king on December 28th, then the period from 28th Dec to Dec 31st is "the year of his becoming king" and from 1st January is his first year. It can be clearly seen from this that the year of his becoming king and his first year are different years.
So the versions on Biblehub which get the Hebrew of this aspect of the verse right are the NIV, New Living Translation, ESV, GNB, Brenton Septuagint Translation, Darby Bible Translation, Young's Literal Translation. In addition my hard copy of the New World Translation gets it right.
Daniel 11:9
The KJV is wrong in Daniel 11:9 which can be compared with other versions at Biblehub.com - the meaning in the NIV, for instance, is correct.
Words with changed meanings
"...but was let hitherto..." (Romans 1:13). What does that mean? It means "but was hindered up to now". "Let" has almost completely reversed its meaning in this verse since the time of the writing of the KJV. There are many other words in the KJV which are obsolete or which have new meanings.
Acts 7:45 "Jesus" should say "Joshua". Also in Hebrews 4:8.
Acts 12:4 "Intending after Easter to bring him forth to the people". This is a strange one, its hard to understand why the KJV translators should have used "Easter" when "Passover" is correct and easily understandable.
Acts 17:22 "I perceive that in all things ye are too superstitious" - should read "very religious" as in the NKJV. Paul is hardly going to start his speech with an insult which is how it sounds to us today.
Acts 19:37 "which are neither robbers of churches" should read "robbers of temples".
In general much value is lost in the KJV in the translation of official titles in the Acts of the Apostles, such as proconsul (13:7,8 & 18:12 - "deputy"), politarchs (17:6 - "rulers"); duumvirs (16:20 & 35 - "magistrates" - "duumvirs" is a higher title than the official title of "praetor" and was undoubtedly used as a higher courtesy title in Philippi, just as it was proven by Sir William Ramsay to have been so used in the surrounding colonies); lictor (16:35 - "sergeants", lictors were typically teenage boys who carried the large symbol of their authority, the fasces lictoriae, when giving messages from the praetors/duumvirs); Asiarchs (19:31 - "chief of Asia"); scribe (19:35 - "townclerk" - see Vine's Dictionary on this and the other titles); temple keeper (19:35 - "worshipper" - the people of Ephesus may well all of them have been worshippers of Diana/Artemis, many others from other towns were too besides the Ephesians. This is not what it means: the city of Ephesus was the "temple keeper", and thus the citizens of Ephesus were the temple keepers (I guess "custodians") of the Temple of Artemis and of the image that fell from heaven); proconsuls (19:38 - "deputies").
Romans 3:3 "shall their unbelief make the faith of God without effect?" - should read "faithfulness of God".
Romans 5:11 "the atonement" - "reconciliation" (Vine's dictionary).
Romans 8:24 "For we are saved by hope" - "for we are saved in hope" (C.H. Spurgeon). Mere hope never saved anyone.
Romans 10:5 "For Moses describeth.." - "For Moses writes about..".
"Describing" can nowadays be done either by writing or by speaking. The option of speaking should be taken away from the reader's mind in verse 5 to maintain the contrast between verses 5 and 6, of "writes" (v5) and "speaks" (v6). (Probably the idea of this contrast is of the nature of the dead letter written on stone and a living faith which therefore speaks.)
1 Cor 9:23 "partaker thereof with you"- "partaker of it" (ie a partaker of the gospel).
These are just a selection of what I think are errors for whatever reason in the KJV. Please could others add to this list with their own, I think it would be helpful to see off this KJV-only heresy which has actually done quite some damage in splitting fellowships, I hear in Singapore.
Oh, and another one to finish with Ezekiel 40:1 "in the beginning of the year, in the tenth day of the month" - though not actually an error it is more accurate to have "on New Year's Day, on the tenth day of the month" or to give the transliteration of "on Rosh Hashanah, on the tenth day of the month". Of course New Year's Day was always on the first day of the month, the day of the appearance of the new crescent moon... except in the Year of Jubilee every 49 years (Leviticus 25:9,10). What Ezekiel is saying is that the year mentioned was a Year of Jubilee. (And the Seder Olam says it was the 17th Year of Jubilee, meaning it was 833 years since the entry into the Promised Land under Joshua.)