Why does the KJV have more verses than my NIV?

Some helpful info on where our Bibles came from, by Justin Taylor (quoting Daniel Wallace):
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Have you ever wondered why modern translations of the Bible don’t have certain verses found in the King James Bible? This can be a sensitive pastoral issue, especially in some regions of the United States.

I occasionally get requests for recommended resources on how to respond, and thought I’d pull together a few popular-level pieces in this post.

Here is New Testament scholar Daniel Wallace:

The Greek text which stands behind the King James Bible is demonstrably inferior in certain places. The man who edited the text was a Roman Catholic priest and humanist named Erasmus. He was under pressure to get it to the press as soon as possible since (a) no edition of the Greek New Testament had yet been published, and (b) he had heard that Cardinal Ximenes and his associates were just about to publish an edition of the Greek New Testament and he was in a race to beat them. Consequently, his edition has been called the most poorly edited volume in all of literature! It is filled with hundreds of typographical errors which even Erasmus would acknowledge.

Wallace highlights two examples, starting with Revelation 22:

In the last six verses of Revelation, Erasmus had no Greek manuscript (=MS) (he only used half a dozen, very late MSS for the whole New Testament any way). He was therefore forced to ‘back-translate’ the Latin into Greek and by so doing he created seventeen variants which have never been found in any other Greek MS of Revelation! He merely guessed at what the Greek might have been.