Calvinists never seem to face 1 John 2:2 head on. It says, "He is the propitiation for our sins: and not for ours only, but also for the sins of the whole world." Calvinists always dismiss the plain meaning of the verse, saying that "whole world" can't possibly mean the whole world, because if it did, it would include trees and mountains and rivers and slugs and termites and other stuff.
Here's what a thoughtful Calvinist might say about 1 John 2:2, without resorting to the "slugs and termites" argument:
The apostle is writing to a primarily Jewish audience. He reminds them that Christ "is the propitiation for our sins; and not for [us Hebrews] only, but also for [the sins of Gentiles from every tongue and nation throughout] the whole world."
Notice, the phrasing of John 2:2 is an exact parallel of John 11:51-52: "He prophesied that Jesus should die for that nation; and not for that nation only, but that also he should gather together in one the children of God that were scattered abroad."
There is little doubt that this is how John's initial audience would have understood this expression. "The whole world" means "people of all kinds, including Jews, Gentiles, Greeks, Romans, and whatnot"as opposed to "ours only"i.e., the Jewish nation.
What the apostle John is saying in the John 11 passage is particularly significant: Christ died so that he might gather "the Children of God"the electfrom the whole world. That is a very clear and explicit statement of so-called "limited atonement."
Understood in its Johannine context, then, a Calvinistic interpretation of 1 John 2:2 seems unavoidable. As one classic work on the atonement says,
The words plainly allude to the atonement as offered and appliedthat is, to the actual expiation, which does not go beyond the number of believing recipients. It is a perversion of the language when this is made to teach the dogma of universal propitiation; or that atonement was equally offered for all, whether they receive it or not, whether they acknowledge its adaptation to their case or not. The passage does not teach that Christ's propitiation has removed the divine anger in such a sense from all and every man. Nothing betokens that the apostle had others in his eye than believers out of every tribe and nation.(George Smeaton, The Apostles' Doctrine of the Atonement, 460).