Standard caveat: I'm new to NT Greek, so please be gentle if my question is silly, basic or obvious.
John 3:16 in the UBS5 is:
Οὕτως γὰρ ἠγάπησεν ὁ θεὸς τὸν κόσμον, ὥστε τὸν υἱὸν τὸν μονογενῆ ἔδωκεν, ἵνα πᾶς ὁ πιστεύων εἰς αὐτὸν μὴ ἀπόληται ἀλλ᾽ ἔχῃ ζωὴν αἰώνιον.
From my understanding of Greek adjectives (this is taken from BBG p.67), the form of
τὸν υἱὸν τὸν μονογενῆ is an attributive adjective. So,
τὸν μονογενῆ modifies
τὸν υἱὸν, which means the whole phrase would be rendered "the unique/only-begotten Son".
And that's where I'm confused. Every single translation I found online (using www.bible-hub.com) renders that phrase as some variation of "His only Son". See here:
New International Version
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
New Living Translation
"For God loved the world so much that he gave his one and only Son, so that everyone who believes in him will not perish but have eternal life.
English Standard Version
“For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.
New American Standard Bible
"For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life.
King James Bible
For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
Holman Christian Standard Bible
"For God loved the world in this way: He gave His One and Only Son, so that everyone who believes in Him will not perish but have eternal life.
I get that logically, Jesus is God's Son. I completely agree with that point and think it's required theology for Christians. That said, I don't see it in the text of this verse.
I do see it in the text of the TR, but in the UBS4 text I have in print and in the UBS5 text online, I don't see any textual variants listed, which makes me believe that there isn't great manuscript support for the
τὸν υἱὸν αὐτοῦ τὸν μονογενῆ reading.
Adding it in seems like an interpretive decision. Am I missing something, or is the reading of this verse so ingrained in English-speaking culture that changing it now is unthinkable?