The typical method used by free-will adherents to prove their teaching that Christ died to provide a potential atonement for each and every person is to cite several scriptures where words like world, every and all, are used.
What is also typical of them is to not look at, and deal with, the context of the verses that they use.
An example of this typicalism #1 is offered to us by Chuck Smith,

We believe that Jesus Christ died as a propitiation (a satisfaction of the righteous wrath of God against sin) "for the whole world" (I John 2:2; 4:9-10), and that He redeems and forgives all who will believe in the death and resurrection of Jesus Christ as their only hope of salvation form sin, death and hell (Ephesians 1:7; I Peter 1:18-19). We believe that eternal life is a gift of God (Romans 6:23), and that "whosoever believeth" in Jesus Christ will not perish, but will have eternal life (John 3:16-18). I Timothy 4:10 says "we trust in the living God, who is the Savior of all men, specially of those that believe." Hebrews 2:9 states that Jesus, "was made a little lower than the angels for the suffering of death, crowned with glory and honor, that He, by the grace of God, should taste death for every man." The atoning sacrifice of Jesus Christ was clearly sufficient to save the entire human race.#2

Before we look at the Scriptures compiled by Mr. Smith, we will look at what God’s word has to say about the death of Christ. To do this, we need only turn to the book of the prophet Isaiah,

But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him: and with his stripes we are healed. All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all.#3

And

Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities.#4

We see that Christ in being wounded and bruised for the transgressions and iniquities of the people #5 results in their being healed. His being an offering for sin results in His seeing His seed. His bearing their iniquities results in their being justified.
It is clear that not everyone will be justified, etc,. It is also clear that the atoning sacrifice of Jesus Christ was sufficient and efficient to save all of those for whom He was the substitute for.#6
Since not everyone will be saved it is obvious that the propitiation mentioned in John’s epistle is not for the whole human race. Otherwise all would be saved and none would be condemned. God’s wrath would be appeased for one and all. Thus, no one would have to experience it.
John is simply saying that Christ is the propitiation for the Jewish believers (the “our”) and the Gentile believers (“the whole world”).#7

In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace;#8

Paul wrote this to “the saints which are at Ephesus, and to the faithful in Christ Jesus.”#9 It is they that have redemption because of what Christ did.
We also observe that not a word is spoken here about man having a free-will opportunity to accept or reject redemption.

Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; But with the precious blood of Christ, as of a lamb without blemish and without spot:#10

It is those that are called #11 that are spoken of here as being redeemed. Once again the doctrine of man having a free-will to be or not to be redeemed is conspicuously absent.

Mr. Smith also mentions that eternal life is a gift of God and cites the following as his reference,

For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.#12

We see that the verse prior to this one says "being made free from sin." Free? Have we at last found the ever elusive free-will of man? Wait! Alas! Not this time...again. For we see that Paul thanks God for their having obeyed, being made free from sin and becoming servants of righteousness.#13 Once again the ever elusive free-will of man remains, well, ever elusive.

As for John 3:16-18, we’ll just point out the following,

For God sent not his Son into the world to condemn the world; but that the world through him might be saved.#14

The Father sent the Son to provide a free-will opportunity for the world...? Wrong! To save the world! Right!

For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe.#15

John Gill points out that this verse is speaking of God as the preserver of all men. He “supports and upholds them in being, and supplies them with the necessities of life...but his providence is extended in a special manner towards [believers].”#16
This fits perfectly with what Paul says here,

...having promise of the life that now is, and of that which is to come.#17

Notice that he mentions the life that is now, temporal, and the life which is to come, eternal.
Plus it would make absolutely no sense at all to say that God is the Savior, in a redemptive manner, of those that are ultimately lost. He’s the Savior of those that are saved and of those that are not saved?

We now come to the last verse used by Mr. Smith as a proof text for his perspective on the atonement.

But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.#18

When we look at the verses that follow verse 9 we see the result of the death of Christ. Many sons are brought to glory,#19 they are sanctified,#20 they are delivered from bondage#21 and there is reconciliation made for their sins.#22
In conclusion, we would have to say that God’s word teaches the complete opposite of what the free-will Calvary Chapel view does on the death of Christ.
The Lord Jesus Christ did indeed save His people from their sins.#23 Let the redeemed of the Lord say, Amen!

My soul, hast thou ever considered one of the sweet properties of justification; not only in the fullness and completeness of it, and in all the several blessings connected with it, as it ariseth out of Jehovah in his own threefold character of persons; all and each taking part in it; but also in that which this portion points out, the nearness in which Jesus, the glorious justifier, always stands to thee, and surrounds thee? Sit down, this evening, and contemplate the subject of justification in this point of view, for it is indeed most blessed. All the persons of the Godhead have, and are engaged in making it effectual to every poor sinner, so as to give the mind always somewhat to rest upon, in the assurance of it. God the Father is the source and fountain of it, not only in having provided it in his dear Son, but also as having by the justification of all the Redeemer's work, to all intents and purposes, justified the poor believer in Jesus. Hence the apostle, with rapture, exclaims: "It is God that justifieth; who is he that condemneth?" Rom. viii. 33, 34. And it is Jesus that justifieth all his redeemed, by his blood and righteousness; "for he was delivered for our offences, and was raised again for our justification;" Rom. iv. 25. And that the hand of God the Holy Ghost was in all this, is equally evident; for it is as expressly said, that Christ was "justified in the Spirit;" which would never have been the case, had not both God's law and God's justice been satisfied, and thus justified Jesus, as the sinner's surety. I Tim. iii. 16. Rom. i. 4. But, over and above these glorious truths, as the foundation of every poor believer's hope, I charge thee to mark it down, my soul, in the memorandums of thine inmost thoughts, that as God the Father, who justified Jesus, thy surety, was always near to him, so he that justifieth thee is always near to thee. The charter of grace, and thy pardon written down in it in letters of blood, even the blood of Christ, is always near and at hand. Here it stands on eternal record," that God is just and the justifier of him that believeth in Jesus." And he is near that justifieth, both as thine advocate to plead, that if any doubts should arise in thy poor timid mind concerning it, Jesus might open the volume of record, and there, by his Holy Spirit, show it unto thee; and also, by the same almighty power, incline thy heart to the perfect belief of it, to thy joy and peace in believing. Now I again charge it upon thee, this night, that thou from henceforth never lose sight of the soul-reviving truth contained in this blessed scripture. But when Satan accuseth, and fears arise, and doubts would creep in, and both law and justice seem to be reviving their claims, look not at thyself, but look to all-precious Jesus. Behold him in all his fullness, suitableness, and all-sufficiency, as thy law-fulfiller and sin-atoning surety, and cry out in those divine words which the Holy Ghost hath given thee," He is near that justifieth me!"

End Notes:
1 An original term coined by ye editor.
2 Calvinism, Arminianism & The Word Of God - A Calvary Chapel Perspective, P. 5.
3 Isaiah 53:5, 6.
4 Isaiah 53:10, 11.
5 Isaiah 53:8.
6 See The GTM Rock Of Grace Exalter, August 2002, Number 18, The Biblical Doctrine Of Substitution, Joseph Irons.
7 See Predestination, Foreknowledge & Salvation, John Gill, Pp. 15 - 21.
8 Ephesians 1:7.
9 Ephesians 1:1.
10 1 Peter 1:18, 19.
11 1 Peter 1:15.
12 Romans 6:23
13 Romans 6:17, 18.
14 John 3:17.
15 1 Timothy 4:10.
16 Of Redemption By Christ, p. 31.
17 1 Timothy 4:8.
18 Hebrews 2:9.
19 Hebrews 2:10.
20 Hebrews 2:11.
21 Hebrews 2:14, 15.
22 Hebrews 2:17.
23 Matthew 1:21.