Question:  Why does AV7 John 3:16 read: "His Only Begotten Son" when so many others read "his one and only son"?

Answer:  "His Only Begotten Son" is correct.
"his one and only son" is not correct.

The reason why this is important:

It is  not true  (not a true statement)  to say that Jesus Christ was God's  "one and only son."  All genuine believers in God and in Jesus Christ are God's children -- sons and daughters who are adopted into God's family and equal heirs to the kingdom of heaven.  Many verses in the Bible atest to this fact.

This is another of the many, many examples why it is so crucially important to preserve word-for-word translation accuracy ... because paraphrases are so often misleading and seriously alter and distort the truth.

In this case, word-for-word translation accuracy clearly reveals what, exactly, it is that makes Yeshua-Jesus Christ unique as the Son of God.  To omit this key word "begotten" and/or to substitute the inaccurate paraphrase "one and only son" is a very serious error.

The Greek word transliterated "monogenh" - has two parts:  "mono" literally means "one" or "only" (not "one and only");  and "genh" literally means "gene."  The word "gene" is defined as, "the basic physical unit of heredity."  It very specifically means from the same genetic line or "begotten" by a biological father.  To omit this crucially important second part of the word "monogenh" significantly alters and distorts the meaning of this verse.

Click this link to view a graphical image that shows word-for-word Greek-to-English.

Compare the verse John 3:16 in other versions of the Bible to see how most other versions omit this crucially important word "begotten."  One resource where you can compare verses in different versions is:  BibleGateway.com