Do the phrases 'all men', 'world' etc. mean the entire human race or even the entire population of a specified area? (Try and substitute those types of phrases in the following verses and you should see that that is not the authors' meaning at all.
When Herod the king heard these things he was troubled and ALL JERUSALEM with him (Matt. 2v3)
Then went out to him Jerusalem, and ALL JUDEA, and ALL THE REGION about Jordan, and were baptized of him (Matt 3v5)
And his fame went throughout ALL SYRIA (Matt 4v24)
And you shall be hated of ALL MEN for my name's sake (Matt 10v22)
And ALL THE PEOPLE were amazed and said, Is this the son of David? (Matt 12v23)
And when he was come unto Jerusalem ALL THE CITY was moved, saying, Who is this? (Matt 21v10)
ALL hold John as a prophet (Matt 21v26)
Then answered ALL THE PEOPLE and said, His blood be on us and on our children (Matt 27v25)
And there went out to him ALL THE LAND of JUDEA and they of Jerusalem and were ALL baptized of him in the Jordan (Mark 1v5)
And ALL THE CITY was gathered together at the door (Mark 1v33)
And when they had found him, they said to him, ALL MEN seek for thee (Mark 1v37)
And ALL MEN did marvel (Mark 5v20)
And when he had called ALL THE PEOPLE unto him (Mark 7v14)
ALL MEN mused in their hearts of John whether he were the Christ or not (Luke 3v15)
ALL THE PEOPLE will stone us for they be persuaded that John was a prophet (Luke 20v6)
Behold the same baptizes and ALL MEN come unto him (John 3v26)
ALL THE PEOPLE came unto him, and he sat down and taught them (John 8v2)
If we let him thus alone, ALL MEN will believe on him and the Romans shall come and take away our place and our nation (John 11v48)
Praising God and having favour with ALL MEN (Acts 2v47)
ALL THE PEOPLE saw him walking and praising God (Acts 3v9)
Many of them which used curious arts brought their books and burned them before ALL MEN (Acts 19v19)
Diana, whom ALL ASIA and the WORLD worships (Acts 19v27)
This is the man that teaches ALL MEN everywhere against the people (Acts 21v28)
For you shall be his witness unto ALL MEN of what you have seen and heard (Acts 22v28)
For your obedience is come abroad unto ALL MEN (Romans 16v19)
WORLD: That ALL THE WORLD should be taxed (Luke 2v1)
If you do these things, show yourself to the WORLD (John 7v4)
Do you perceive how you prevail nothing? Behold, the WORLD is gone after him (John 12v19)
These that have turned the WORLD upside down are come hither also (Acts 17v6)
Diana . . . whom all Asia and the WORLD worships (Acts 19v27)
Your faith is spoken of throughout the WHOLE WORLD (Romans 1v8)
That we should not be condemned with the WORLD ( 1 Cor 11v32)
And ALL THE WORLD wondered after the beast and they worshipped the dragon (Rev 13v3)
What does it mean? Let the Bible speak!
He prophesied that Jesus should die for that nation, AND NOT FOR THAT NATION ONLY, but that also he should gather together in one the children of God that were scattered abroad (Luke 11v51-52)
You were slain and have redeemed us to God by thy blood OUT OF EVERY KINDRED and TONGUE and PEOPLE and NATION (Rev 5v9)
Many take verses out of context and read them as isolated texts. We should all be aware of that. The Bible is especially in the NT a collection of letters written to believers. The Bible is not written to the unbelievers, so when we see words such as 'us', 'we', 'beloved' etc etc, we should say, Paul etc is addressing believers here, not the world at large.
'For I say through the grace of God given to me, to every man THAT IS AMONG YOU, not to think more highly than he ought to think but to think soberly, according as God has dealt to every man the measure of faith' (Romans 12:3)
Now, it should not be necessary for me to point out that when Arminians [not all, but many I have met] claim this means that all men in the world have faith, and that it is up to each individual to use his 'portion' aright that this is NOT what Paul is saying. He said 'every man among you' and it would be superfluous to repeat 'among you' with the 2nd 'every man'. He is talking about the church.
Again, Colossians 1:28 'Whom [Jesus] we preach, warning every man, and teaching every man in all wisdom, that we may present every man perfect in Christ Jesus' The 'every man' phrases are not universal here either. To say so is absurd.
Now, when we come to WORLD and ALL [and the reason I posted that list of texts was to show how those words are used by the Holy Spirit in the Bible] we need to remember what I have just said.
The NT was written to people who believed that God was the God of the Jews ONLY and that the Gentiles were accursed John 3:16 was spoken to a Pharisee who held that opinion. To correct this error, the apostles and Christ used words such as 'the world' [Jews and Gentiles collectively, people of all nations] and 'all men' [men of all classes and types, from all nations]. In some texts the term is obviously 'all of US' or all believers or all the elect. That is especially true of 2 Peter 3:9 where 'longsuffering to us-ward' is deliberately emphasised.
Now, I would like to ask the Arminian if words have meaning. They criticise Calvinists for re-interpreting 'world' and 'all men' for their own purposes. But what do the words 'propitation' [1 Jn 2:2], 'taketh away sins' [Jn 1:29], 'tasted death' [Heb 2:9], 'Saviour' [John 4:24] mean?
Is a propitiation where God still retains His wrath and sends the objects of that propitiatory sacrifice to hell?
Is a Saviour someone who makes salvation possible?
Does tasting death mean that the sinner must still drink the dregs of God's wrath himself?
Does 'taketh away sins' mean that sins are still here, and God still sends people to hell for them?
You see the dilemma that words bring? Atonement, Redemption, Satisfaction, all such terms are robbed of their meaning by the Arminians.
