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It's good that you have brought this up.. Begotten and monogenes .. "only begotten" translates the Greek word monogenes. This word is usually translated into English as "only," "one and only," and "only begotten." It's the "only begotten" translation that gives the wrong impression that Jesus was begotten in the human sense of procreation.. When it is very clear that no one ever thought it meant this.. As that would not have been construed from the term "monogenes". You could ask yourself why the Quran admonishes Christians of the time for believing Jesus was " begotten" when they certainly would not have inferred that idea from the scriptures. They would have inferred from the term monogenes the uniqueness of Jesus in that their was no one like unto Him.
In early Christian Literature, monogenes has two primary definitions. The first definition is "pertaining to being the only one of its kind within a specific relationship." You are correct in your information about is its meaning in Hebrews 11:17 when the writer refers to Isaac as Abraham's "only begotten son". Abraham had more than one son, but Isaac was the only son he had by Sarah and the only son of the covenant. So it is the uniqueness of Isaac among the other sons that allows for the use of monogenes in that context.
The second definition is "pertaining to being the only one of its kind or class, unique in kind." This is the meaning that is implied in John, which was primarily concerned with demonstrating that Jesus is the Son of God (John 20:31), and he uses monogenes to highlight Jesus as uniquely God's Son—sharing the same divine nature as God—as opposed to believers who are God's sons and daughters by adoption. Jesus is God’s “one and only” Son.
You are correct when you say Jesus was unique in many ways.. Where you are maybe in error is that you don't ask the important question... Why? Why was only Jesus out of all the prophets unique? Could it be He was the promised Messiah? The one sent to redeem mankind and correct the fall of Adam.. So making us once more right before God.. I believe He was... Jesus was everything He said He was. Never a lie was found on His lips, do you think He would have accepted worship as God and let people believe He shared a unique relationship with God if it were not so?