Everyone Believes the Atonement is Limited
Since all are not redeemed in the end, even Arminians believe the atonement is limited. Both Reformed and non-Reformed believe that only some of the ill-deserving persons on earth will partake of the benefits of Christ's redemption. Both Reformed and non-Reformed declare that the benefits of Christ's atonement are available to all who believe. The difference is that particular redemption is saying that the redemptive benefits of the atonement will only be applied to that portion which is God's choosing from the mass of ill-deserving persons on the earth. Arminians, on the other hand, believe that the atonement will be applied only to those ill-deserving persons of man's own choosing. But again, what benefit is the atonement to those who are not saved? None which are redemptive. Christ knew before the world existed who would never benefit so it would be contradictory to say he died for all with some kind of hope that the future would be otherwise.