Fido's quote of John Owen summarizes why I believe in Limited Atonement.
HT: Dan Phillips
(I think it was easier to arrive at this for me than for most, and that may be because of growing up with a father who was involved in law enforcement. If we understood anything, it was distinctions between justice, mercy, and grace, & the letter vs. spirit of the law).
Let's look at it briefly
John Owen says that Christ died for either:
1) Some of the sins of all men.
2) All the sins of all men.
3) All the sins of some men.
Limited atonement doesn't mean Christ's blood wasn't sufficient to pay for the sins of all sinners; instead, it asserts that Christ's blood pays for the sins of all believers. In other words, it saves everyone it was meant to save.
But the tipping point for me, I think, was this: if Christ paid for sins of any man, how is a just God justified in having a man also pay for those sins himself? If Christ's blood is truly sufficient to save whosover will come, why is it not able to save some?
The answer, given the nature of God's justice, and the language of justification in the NT, is that Christ died only for those he saves. Anything else would be a cosmic miscarriage of justice.