There are generally two primary views on the Atonement in Protestant Evangelical circles: (1) that the aim of the atonement was to make all men savable, and (2) the aim of the atonement was to save some men. Theologian Louis Berkhof frames the issue this way:
The question with which we are concerned at this point is not (a) whether the satisfaction rendered by Christ was in itself sufficient for the salvation of all men, since this is admitted by all; (b) whether the saving benefits are actually applied to every man, for the great majority of those who teach a universal atonement do not believe that all are actually saved; (c) whether the bona fide offer of salvation is made to all that hear the gospel, on the condition of repentance and faith, since the Reformed Churches do not call this in question; nor (d) whether any of the fruits of the death of Christ accrue to the benefit of the non-elect in virtue of their close association with the people of God, since this is explicitly taught by many Reformed scholars. On the other hand, the question does relate to the design of the atonement. Did the Father in sending Christ, and did Christ in coming into the world, to make atonement for sin, do this with the design or for the purpose of saving only the elect or all men? That is the question, and that only is the question.
In discussing these issues with folks who have a high view of man, you hear it stated that the Calvinist view is based purely on inference and logic and has no Biblical support. My intention here is not to cover everything the Bible says about Atonement, there are too many quality works that do that, but rather to provide a handful of Biblical passages that assert that Christ’s First Coming and Death had a definite purpose.
God Has a Purpose
The first thing, in my opinion, that must be dealt with is the understanding that God has an eternal plan and purpose for the things that happen in this world.
In whom also we have obtained an inheritance, being predestinated according to the purpose of him who worketh all things after the counsel of his own will... (Eph 1:11)
What things does God work according to his will? All things. What about bad things or things we don’t like? Well, the Scriptures teach us that God is good and that He doesn’t like bad things either. But, either bad things happen because they are a part of God’s larger plan for good, or they happen randomly, without purpose, and not in accordance with God’s purpose and plan. When we come to the realization that God is God and that His authority and purpose rules sovereign over all things, it transforms the way we see God, Scripture, and ourselves!
The People Christ Redeemed (Purchased) Are His Elect
Who does god justify? Those who He has predestinated. And for those he will provide everything essential to their salvation and sanctification.
Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified. He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things?
Continuing with Romans 8, we that Christ died for, loves, keeps, and makes intercession for us believers.
Who shall lay any thing to the charge of God's elect? It is God that justifieth. Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us. Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution...
The Good Shephard lays down his life for his sheep.
I am the good shepherd: the good shepherd giveth his life for the sheep ...As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep. (John 10:11-15)
Christ gave Himself for the church.
Take heed therefore unto yourselves, and to all the flock, over the which the Holy Ghost hath made you overseers, to feed the church of God, which he hath purchased with his own blood. (Acts 20:28)
Husbands, love your wives, even as Christ also loved the church, and gave himself for it; That he might sanctify and cleanse it with the washing of water by the word, That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish. (Eph 5:25-27)
Christ gave Himself for Believer’s Sins
[Christ] gave himself for our sins, that he might deliver us from this present evil world, according to the will of God and our Father (Gal 1:4)
But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. Much more then, being now justified by his blood, we shall be saved from wrath through him. (Rom 5:8-9)
[Christ] gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works. (Tit 2:14)
Greater love hath no man than this, that a man lay down his life for his friends. Ye are my friends, if ye do whatsoever I command you. (John 15-13-14)
For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him. (2 Cor 5:21)
For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God (1 Pet 3:18)
Christ hath redeemed us from the curse of the law, being made a curse for us (Gal 3:13)
[Christ] bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed (1 Pet 2:24)
The Definite Scope of Christ’s Priestly Work
The priestly role of Christ is not limited only to providing a sacrifice, but also providing intercession. For whom does Christ intercede?
Who shall lay any thing to the charge of God's elect? It is God that justifieth. Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us. (Rom 8:33-34)
I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and they have kept thy word. ...I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine. ...Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are. ...Neither pray I for these alone, but for them also which shall believe on me through their word... (John 17)
But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin. (1 John 1:7)
Several verses in the New Testament appear make applicability of Christ’s atonement to the world, but there are many that specifically limit it to ‘many’.
Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many. (Mt. 20:28)
For this is my blood of the new testament, which is shed for many for the remission of sins. (Mt 26:28)
And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. ...So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation. (Heb 9:15-28)
Perhaps the Arminian would not be convinved by these arguments, clinging tenaciously to 1 Jn 2:2 as overthrowing all, at least let him not say we have no Scriptural basis for our argument. I found these in about 15 minutes of work. MUCH more could be said, but this should be sufficient for the present cause.