SimpleI'm not going to take a stand on whether or not atonement is limited or sufficient for all because I honestly don't know.
I'd just like to hear from non-Calvinists as to how they reconcile their view of atonement with the fact that not all people will be saved. Isn't that, by definition, limited atonement? Or is there another explanation?
As even the Calvinist Shedd notes
It may be asked: If atonement naturally and necessarily cancels guilt, why does not the vicarious atonement of Christ save all men indiscriminately, as the universalist contends? The substituted suffering of Christ being infinite is equal in value to the personal suffering of all mankind; why then are not all men upon the same footing and in the class of the saved, by virtue of it? The answer is because it is a natural impossibility. Vicarious atonement without faith in it is powerless to save. It is not the making of this atonement, but the trusting in it, that saves the sinner: “By faith are you saved” (Eph. 2:8); “he that believes shall be saved” (Mark 16:16). The making of this atonement merely satisfies the legal claims, and this is all that it does. If it were made but never imputed and appropriated, it would result in no salvation. A substituted satisfaction of justice without an act of trust in it would be useless to sinners. It is as naturally impossible that Christ’s death should save from punishment one who does not confide in it as that a loaf of bread should save from starvation a man who does not eat it. The assertion that because the atonement of Christ is sufficient for all men therefore no men are lost is as absurd as the assertion that because the grain produced in the year 1880 was sufficient to support the life of all men on the globe therefore no men died of starvation during that year. The mere fact that Jesus Christ made satisfaction for human sin, alone and of itself, will save no soul. Christ, conceivably, might have died precisely as he did and his death have been just as valuable for expiatory purposes as it is, but if his death had not been followed with the work of the Holy Spirit and the act of faith on the part of individual men, he would have died in vain.[1]
[1] William Greenough Thayer Shedd, Dogmatic Theology, ed. Alan W. Gomes, 3rd ed. (Phillipsburg, NJ: P & R Pub., 2003), 726.