Here’s a fifth reason Pink gives for thinking 1 John 2:1-2 conclusively doesn’t teach unlimited atonement (You can refer to the previous posts for the other reasons, as well as a little bit of background involved in this debate). Here’s Pink in his own words:
In the fifth place, the above interpretation is confirmed by the fact that no other is consistent or intelligible. If the "whole world" signifies the whole human race, then the first clause and the "also" in the second clause are absolutely meaningless. If Christ is the propitiation for everybody, it would be idle tautology to say, first, "He is the propitiation for our sins and also for everybody". There could be no "also" if He is the propitiation for the entire human family. Had the apostle meant to affirm that Christ is a universal propitiation he had omitted the first clause of verse 2, and simply said, "He is the propitiation for the sins of the whole world." Confirmatory of "not for ours (Jewish believers) only, but also for the whole world"—Gentile believers, too; compare John 10:16; 17:20.
Pink argues that his interpretation is the only one that is consistent, seeing that John’s statement would be redundant or unintelligible. If John means by “the whole world” everybody in it, then this would obviously include the “for our sins only.” However, the us seems to be in addition to “the whole world,” therefore one can only take John as meaning Jews and Gentiles.
This seems pedantic. For example, if I gave my daughter a mini pizza sliced four ways, she having eaten one piece, I might firmly command her, “Eat the whole pizza.” This doesn’t negate that there’s ¾ of the pizza left and that my daughter has consumed ¼ of it. It would be silly for my daughter to protest, “I can’t eat a whole pizza in addition to the slice I had,” as if what I meant was for her eat 4/4 of the pizza in addition to ¼ of another pizza. The ¼ is included in my command to eat the whole thing. In the same way, the Christians that John is addressing are included in the whole world. Pink’s charge of idle tautology is true only if John was trying to delineate his claims in formal logic. Everyone concedes that language is far more fluid.