4 point calvinism, Amyraldianism, Christmas Calvinist(noel(no L)), Unlimited Limited Atonement

These are all names for a theological system that holds to 4 of the 5 points of calvinism.

Total Depravity, Unconditional Election, [Limited Atonement], Irresistible Grace, Perseverance of the Saints.

They claim to object to Limited Atonement, however when you listen to some of their philosophical objections(they do have biblical objections as well), their philosophical objections usually revolve around the following idea in one way or another.

“Limited Atonement means that there can be some people who are repenting and believing and begging God for salvation who will not be forgiven by God.”

However this statement is opposed not to limited atonement, but to Unconditional Election. The objection is that there are certain people whom GOD HAS NOT CHOSEN. This is what they object to. If they believed this, then they wouldn’t have an issue with God not dying for the people whom he already didn’t choose.
Secondly there is an unspoken belief in this system that man can repent and believe without the Holy Spirit regenerating. They don’t believe man is incapable of repenting.

Come back later for a biblical examination of Limited Atonement according to the Book of Hebrews.