When I have considered the debate on whether the atonement is "limited" or "unlimited" it has always baffled me why it is really a debate for true blue orthodox Christians. The word "limited" itself is oftentimes misinterpreted because people either think you are limiting the power of the atonement or limiting the gospel message to a chosen few. This gives us another reason why we should be precise with our language and seek to avoid words that can convey a distorted message. Even with that being the case, when someone says (like me!) that they believe in limited atonement, they do NOT mean the gospel message is proclaimed to a limited number of people, nor do they mean the power is limited in the least bit. But what they do mean is the application of the atonement is limited.
This is why I prefer to say I hold to particular redemption or definite atonement. Both phrases better convey what is meant by "limited" atonement, although they do ruin the TULIP acrostic many of us love (it is such a pretty flower:).
What do they convey and why isn't every dyed-in-the-wool believer on board with the better terminology? The second question I can't fully answer, but in reality every true believer to a degree does believe in a particular redemption. Why? Because every true believer does NOT believe in universalism and they believe it is only through the blood of Jesus that Christians are saved (What can wash away my sins, Nothing but the blood of Jesus!). The phrases clearly convey that when Christ died on the cross and propitiated the wrath of God on behalf of sinners, bearing their sins, atonement was definitely, 100% made and therefore only a particular amount of people would be redeemed by that atonement. Otherwise, everyone would be in heaven since there is no more wrath of God against mankind, nor sin to be accounted for. Some may say, "That is Calvinist logic! There is nothing of the sort in the scriptures!" Is that so?
Go to my studies here and here which lays out what I believe is a strong Biblical, exegetical case for a definite atonement and particular redemption. If that is not enough, check out this lengthy and IMO irrefutable article by Brian Schwertley here.
One last thought to consider. If you are a Christian reading this, your sins have definitely been atoned for, correct? YES, you say. A second question then, have they been definitely atoned for in the same way a non-believer's sins have been atoned for? If you say, YES, then your God could bring your sins up against you on the last day the same way he will bring the non-believer's sins against them on the last day. For God will condemn the non-believer based on his sins.
Praise God that will not ever happen! His never-failing, irrevocable atonement not only forgave our sins, but gave us the promise that God will NEVER bring them back up again to condemn us. Psalm 103:12 As far as the east is from the west, so far does he remove our transgressions from us.
Blessed be the Name of the Lord for His indescribable gift!