If Christ died for all, why do not all enjoy the benefits of His work? Is it because they did not meet the condition for the enjoyment of His fruits, namely, faith? Well, Scripture testifies and we believe, that the condition itself, faith, is a fruit of His merit (see here). His work on the cross provides the condition for the enjoyment of its benefits. But this is not the case with the position of the opposing party.
Substitutionary Atonement (Arg. XV)
That beautiful doctrine of substitutionary atonement is a Reformed doctrine. It is inconsistent with Arminianism. The doctrine teaches that Christ bore the sins and stood in the place of everyone for whom He died, so as to take their penalty upon Himself. He made payment to the Father with His blood and purchased His Bride (e.g., Acts 20:28). The problem for the Arminian view of the atonement is that it has Christ dying in the same way for both elect and reprobate. In the non-Calvinistic view, the atonement does not provide the condition for its enjoyment, namely, faith. According to the non-Calvinistic view, the Lord Christ on the cross bore the sins and took the place of the reprobates even as He took the place of those who were chosen from before the foundation of the earth. Alas! Even though the Lord died in the same way for the elect as well as the reprobates, one group will believe but the other will not. It is obvious that in this scheme the deciding factor does not lie with the Lord, but with the free will of man. The atonement is not effectual in and of itself, but requires the assistance of man. Even if a reply would come to us that the faith of man will count only for 1% or even less, the fact is clear: without that 1%, the atonement, which was made on your behalf, is useless. Furthermore, this atonement does not provide the condition for its enjoyment but leaves that to the wretched sinner himself.
Dr. Owen in his own words:
The very phrases of “dying for us,” “bearing our sins,” being our “surety,” and the like, whereby the death of Christ for us is expressed, will not stand with the payment of a ransom for all. To die for another is, in Scripture, to die in that other’s stead, that he might go free; as Judah besought his brother Joseph to accept of him for a bondman instead of Benjamin, that he might be set at liberty, Gen. 44:33, and that to make good the engagement wherein he stood bound to his father to be a surety for him. He that is surety for another (as Christ was for us, Heb. 7:22), is to undergo the danger, that the other may be delivered...And this plainly is the meaning of that phrase, “Christ died for us;” that is, in the undergoing of death there was a subrogation of his person in the room and stead of ours...But concerning the word ἀντί, which also is used, there is no doubt, nor can any exception be made; it always signifieth a commutation and change, whether it be applied to things or persons: so Luke 11:11, Ὄφις ἀντὶ ἰχθύος, “A serpent instead of a fish;” so Matt. 5:38, Ὀφθαλμὸς ἀντὶ ὀφθαλμοῦ “An eye for an eye;” so Heb. 12:16; — and for persons, Archelaus is said to reign ἀντὶ Ἡρώδου τοῦ πατρός, “instead of his father,” Matt. 2:22. Now, this word is used of the death of our Saviour, Matt. 20:28, “The Son of man came δοῦναι τὴν ψυχὴν αὑτοῦ λύτρον ἀντὶ πολλῶν,” — which words are repeated again, Mark 10:45, — that is, to give his life a ransom in the stead of the lives of many. So that, plainly, Christ dying for us, as a surety, Heb. 7:22, and ...