Limited Atonement, the L in Calvinism's TULIP, is the belief that Christ's sacrifice on the cross does not atone for the sins of the whole world, but rather, only for the elect. This is the hardest Calvinistic doctrine to defend, the easiest to refute, and most commonly rejected by 4 point Calvinists.
With the wealth of scriptures that conflict with Limited Atonement, it almost seems unnecessary to argue deductively against it. Nevertheless, it is possible to do so. One way of doing so is to select a random person who died in their sins. For purposes of this article, I chose Christopher Hitchens.
Christopher Hitchens was a famous atheist, right up until his tragic death in December of 2011. There is no evidence that He ever repented, and so it is safe to assume he did not. Christopher Hitchens died outside of Christ, his sins are retained, and he is destined to spend eternity in Hell. The question we must ask is did he have to?
Biblically speaking, one must contend the answer is no. If Christopher Hitchens, at any point before his death, had repented of his sins, confessed Jesus as Lord, and sincerely believed God raise Him from the dead, scripture assures us he, too, would have been saved. He would not have been rejected because he was not among the elect, nor because Christ's sacrifice was not sufficient to cover his sins. There would be no need of a new sacrifice, and God would not need to remove a single person from the elect to account for him. His salvation would be identical to every other Christian.
At this point, the Calvinist might object and say that Christopher couldn't have repented precisely because he was not elect. But this dodges the question. We can deal with Total Depravity some other time (see both the Calvinism vs. Arminianism and Moral Objections sections for articles I've already written about free will). If I said "you would die if I shot you in the head", the fact that I don't have a gun or unobscured line of sight does not make you bulletproof nor immortal. In the same way, even if you want to argue it was impossible for Christopher Hitchens to have repented, the fact that he would have been saved if he had repented means Limited Atonement is an unsustainable doctrine.
As long as faith is the sole criteria for salvation, which most Calvinists acknowledge, then the atonement must cover all sinners who could potentially come to faith. It cannot cover those who die outside of faith, so there goes the argument that we must accept either Limited Atonement or Universalism, but it must cover the sins of the whole world, first of all because the Bible says it does (e.g. 1 John 2:2), but also because if it didn't, there are people who could potentially fulfil the requirements for salvation, but apparently, the death and resurrection of God's only begotten Son is somehow insufficient to follow through on His promise. If we believe "whosoever believeth in him should not perish, but have eternal life" (John 3:15), it is imperative that we reject Limited Atonement.