Arminians have always had their objections to the Reformed doctrine of Limited Atonement - or as it is sometimes known - Particular Redemption. Essentially this doctrine tells us that Christ's death was an atonement paid particularly for the Elect alone. Whether or not Christ's death has any reference or effect upon those who are not elect is of little importance. He did not die for everyone equally in the same way. Scripture is plain that Christ died for His Church, for His sheep. Not everyone is a member of His Church; not everyone is a sheep. Christ told some of His listeners, to their faces, that they were not of His sheep. Arminians claim that we limit the power of the atonement by not letting it apply to all men equally. We say they limit it even more so by evacuating its efficacy. Calvinism says Christ died to save His people from their sins. Ariminianism says that Christ's death made salvation possible for all men. Nevermind the obvious problem that if Christ died for all men's sins equally, then no one should go to Hell, since salvation necessarily entails forgiveness of sins; but think of the more serious ramification of saying Christ died for what turns out to be a lost cause for millions of souls.
As I noted, Arminians have put forward objections to this doctrine. I intend to tackle the main ones, and give several answers to them from Scripture.
Objection 1. What everyone is bound to believe must be true, and it is the duty of all men to believe; therefore Christ must have died for all men.
Answer 1. OK, suppose we grant this position, wouldn't the doctrine of discriminating love be destroyed by this? What comfort would it be to a soul in distress or trial to believe that Christ died for him in the same way that He did for Judas and all the damned souls in hell?
2. The people to whom the Gospel has never come, they who have never heard of the death of Christ, are not going to believe that Christ died for them (missionary endeavor excepted, of course). What God reveals is true; but God has nowhere revealed that it was His intention that Judas would believe, or that all will believe. God made His covenant with Abraham's descendants. The Canaanites never heard the message of God's grace. They were, nonetheless, destroyed for their sins.
3. Not everyone has the Gospel preached to them. This is what I alluded to above in referring to the Canaanites. But more than that, many to whom it is preached only hear it with the outward ear. In other words, it makes no impression upon their souls unto salvation. They do not sense their state as sinners. They are not weary and heavy laden because of sin. The Gospel proclamation of redemption through Christ's blood is not a joyful sound to them. They don't think they need it. True repentance is the gift of free grace and faith is the gift of God. What is God's, as a gift to bestow, cannot be man's duty to perform as a condition of salvation. Those who are invited to look to Christ, to come to Him for salvation, Scripture describes as weary and heavy laden with sin, penitent, hungry and thirsty, etc. They are invited to come to and believe in Christ, and not all men (Matthew 11:28; Isa 55:1; Mark 2:17).
Objection 2. The words "all" and "every," often used in Scripture, must be taken universally.
Answer 1. The proper way to take "All" and "every" is not in the sense of a universal - for every man individually, in the commonly quoted scriptures. They are to be taken distributively, meaning "of all kinds or types," rather than "every individual." For instance, in Matthew 9:35, we are told that Christ went about healing every sickness and every disease among the people: that is, any and every kind of disease. Christ did not heal every single sick person in Judaea. Also in Colossians 1:28, where "every" is taken distributively three times, and so must be restricted to those to whom Paul preached.
2. "All" in 1 Timothy 2:4, cannot be taken for every man individually, since it is not the will of God that all men in this large sense should be saved: for it is His will that some men should be damned, and justly at that, for their sins and transgressions. Unto some men it will be said, "Depart, ye cursed, into everlasting fire." If God wills all men to be saved, then all men will be saved, for "He (God) doeth according to His will in the army of Heaven, and among the inhabitants of the earth" (Daniel 4:35). God does not fail. He cannot be disappointed in His own will, for He works all things after the counsel of it. Then again in Hebrews 2:9, Jesus is said to "taste death for every [man];" which is in the very next verse restricted to "sons brought to glory." Hebrews 2:11 calls them "sanctified" ones. 1 Timothy 2:6 ("who gave Himself a ransom for all") is rendered in the parallel text Titus 2:14, "who gave Himself for us." Who are the people called "us" in this text? Are they not particularized as "redeemed from all iniquity, purified and made a peculiar people?" Christ gave Himself as a ranson for "all" who fit this description, and for none else. David said, "All men are liars." Take that word in the Arminian sense and you will have made David a liar for saying so.