Well, they get hung up on the word 'world'. To them, that word means 'everybody whoever lived, all w/o exception'. Yet, I can only find one place(not saying there aren't other places, I just haven't found them yet) that 'world' means everybody w/o exception, all whoever lived.
He was in the world,
and the world was created through Him,
yet the world did not recognize Him.[John 1:10]
Ἐν τῷ
κόσμῳ ἦν, καὶ ὁ
κόσμος δι’ αὐτοῦ ἐγένετο, καὶ ὁ
κόσμος αὐτὸν οὐκ ἔγνω[John 1:10 SBLGNT]
kosmo is used once and kosmos is used twice, which does mean 'world'. Now, let's break this verse down...
He was in the world...
So, this is referring to His time here on earth, during His earthly ministry. So, by using their logic, He was with all whoever lived, all w/o exception, while He was living here on earth. But that is not the case, so kosmo here can not mean all whoever lived, all w/o exception.
and the world was created through Him,
Here is the one place where I think 'world' means all whoever lived, all w/o exception, seeing that everything created, including us, He created[John 1:3].
yet the world did not recognize Him.
Again, by using their logic, all whoever lived, all w/o exception, did not recognize Him...even those of us who were born after He ascended to the Father. Even those who walked with Him, served, worshipped and praised Him, did not recognize Him, if 'world' means all whoever lived, all w/o exception.
“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.[John 3:16]
Οὕτως γὰρ ἠγάπησεν ὁ θεὸς τὸν
κόσμον ὥστε τὸν "υἱὸν τὸν μονογενῆ ἔδωκεν, ἵνα πᾶς ὁ πιστεύων εἰς αὐτὸν μὴ ἀπόληται ἀλλὰ ἔχῃ ζωὴν αἰώνιον.
Kosmon is used here which is another form of kosmos and it means world as well.
Now, if 'world' means all whoever lived, all w/o exception, then we see the Christ going rogue at Gethsamane. He prays
"I pray for them. I am not praying for the world but for those You have given Me, because they are Yours."[John 17:9]
ἐγὼ περὶ αὐτῶν ἐρωτῶ· οὐ περὶ τοῦ
κόσμου ἐρωτῶ ἀλλὰ περὶ ὧν δέδωκάς μοι, ὅτι σοί εἰσιν,
Kosmou is another form of kosmos and it also means world. With God, we have a triune Godhead, a Trinity, that is in complete agreement, absolute harmony with each other, with no discord whatsoever. But here Jesus is not praying for the world. By using their logic, He is not praying for all whoever lived, all w/o exception, and is not praying for those the Father loves, if He loves the world and world means all whoever lived, all w/o exception.
So, they are advocating a Trinity that is at odds with each other.