Why is it important to define the Atonement as limited or unlimited?
You asked why we should make a fuss over limited/unlimited atonment, in light of the greater issues around the doctrine of the atonement. In answer, let me agree that there are more important issues regarding the atonement of Christ than its extent (limited or unlimited). For instance, the Anselm view vs. the Abelardian view is much more important: Anselm argued that Jesus died to make satisfaction for our sin, the heretic Abelard argued that Jesus died to show us how much God loves us and inspire us to live him too. The Abelardian view is back among us in various nuances, and must be vigorously rejected. To deny that the atonement accomplishes satisfaction for our sin is to be anti-Christian. In short, the most important issue by far in regards to the atonement is that we vigorously affirm Christ's death as a vicarious, substitutionary atonement to make satisfaction for our sin before God. It is because of this priority that one does not hear much about limited vs. unlimited atonement today: we are now fighting over evangelical essentials, so a doctrinal battle that is de facto between evangelicals is not going to be as important.
Nonetheless, if one is asked, limited atonement cannot be safely discarded or neglected. This is one of those doctrines that is mostly important because of its implications. If you teach a general atonement, you end in numerous kinds of trouble. By limited atonement, we do not deny the infinite value of Christ's blood, nor its efficacy in cleansing us from sin (in fact, the doctrine serves to establish these). The "limited" of limited atonement has to do with its "extent" -- that is, how many people and kinds of people benefit from Christ's atoning death. The "unlimited" or "general" atonement position -- a pillar of Arminian theology -- holds that Jesus died for the sins of everybody in an equal sense. Jesus died for the sins of you the Christian, and he died for the sins of your neighbor the non-Christians, and he did so in exactly the same way. So what determines whether or not someone is saved? Surely not God's sovereign choice or Jesus' discrimination among sinners! Rather, the only thing that causes someone not to be justified is that they did not choose to receive Christ's priceless gift. "Jesus has put the amount needed to pay for everyone's debt in the bank -- now you just have to go open up an account."
Let me give you reasons to reject general or unlimited atonment and to affirm limited atonement:
1) General atonement is not biblical. The Bible never affirms that Jesus died for everyone equally (and Reformed theologians have very adequately addressed the "world" and "all " passages so frequently cited here.) But the Bible does affirm that Jesus did not redeem the world in general, but only the elect (who are also those who receive him in faith). For passages that generally support limited atonement, see Mt. 20:28; Heb. 9:28; Isa. 53:8; Mt. 1:21; Eph. 5:25. Also see Mt. 7:13; 2 Cor. 4:3, 4; 2 Th. 2:10,11; Jude. 4; Rev. 20:11-15 for passages that deny that all will be saved; see also Jn. 17:6, 9, 19, and 24, where Jesus prays to the Father in terms that clearly show that he came to redeem only the elect.
2) General atonement denies the the efficacy of Christ's atonment. Both Arminians and Calvinists teach limited atonement in some sense. Calvinists teach that Christ's death was unlimited in its efficacy for the elect -- it saves God's people utterly. We argue that it is limited in terms of its extent -- that is, the number of people who will benefit from its saving effects. Arminians see the atonement as being unlimited in its extent -- everyone equally benefits from it -- but limited in its efficacy -- it only does so much good for anybody. As they preach it: "Jesus did his part; now you have to do yours." This is an offense to the Bible's teaching regarding Christ's work. According to Scritpure, Jesus came into the world with a definite people in mind for his redemptive work; he died for his own -- for his bride, for the church -- and his death is wholly effectual for the atonement of Christ's own. See Mt. 1:21; Eph. 5:25; Jn. 6:3-40; Jn. 17:6.
3) General atonement robs Christ of his glory, by asserting that he needs us to complete his work. Notice how the Scriptures refer to Christ's saving work in definite and wholly effectual categories. It is Jesus who saves us utterly; not Jesus who did his part but now looks to us to complete it, lest he died in vain. See (Rom 5:10; 2 Cor. 5:18-19; Gal. 3:13; Gal. 4:4; Heb. 9:27).
4) General atonement assaults the doctrine of election. Indeed, unconditional election and limited atonement are tethered together inseparably. To deny that Christ died for a particular people is to deny that God has an elect people for whom he sent Christ to die and rise again. To say that limited atonment is not an important doctrine to defend is to say the same of sovereign election. And to say that is to redefine the gospel in a man-centered direction.
5) General atonement wrongly asserts that liimited atonement speaks to the world with an ingenuine offer of salvation. "After all, if Christ only died for the elect, then how can the Bible say, "Whoever will, let them come?" To argue this is to confuse categories. Christ does offer all a free pardon of their sins if only they will come, and we should speak this way to the world in his name. But it remains true that "No one comes to me unless the Father draws them" (Jn. 6:44). If only the elect are saved -- as the Bible teaches -- and if the Triune God knew these from before the creation of the world -- as the Bible teaches -- and if the precious blood of Jesus cleanses us from all our sins -- as the Bible teaches -- then it is only applied to those elect persons who reveal their election through their faith in Jesus, which is itself the gift of God. This limited number of persons receives an unlimited atonement. Everone else dies in their sins, all of them having known and sinfully rejected God (Rom. 1:18-25) and many of them having spurned a genuine offer from Christ to come to him and be saved.