Since the tea isn't quite ready, I'll try a thumbnail sketch. Remember, Calvinists, I'm not an Arminian. Remember, Arminians, I'm not a Calvinist.
The debate is often neatly framed by the old-fashioned Calvinist acrostic, TULIP. I'll try to be fair to both sides and present what I'd say. Maybe there's a dyed-in-the-wool Lutheran out there who will tell me how heterodox I am too (hints to the Lutheran people I know look at this blog).
T - Total Depravity - The Calvinist affirms that as a result of the Fall, all people are totally depraved. This does not indicate they are absolutely as bad in every way as they possibly can be, but that evil has permeated all their being. Many Arminians will affirm this as well, though some fall into semi-Pelagianism which indicates that people learn to be evil. This is most clearly seen among those who suggest there is an age or developmental level before which God will not hold us accountable for our sin. With the Calvinist, I would affirm depravity, absolutely and completely.
U - Unconditional Election - The Calvinist will affirm that the elect are chosen by God, before the foundation of the world, to be redeemed in Christ, regardless of their own inclinations. The Arminian will normally explain some way that God foreknows who will believe and then elects those people. I frankly can't come up with a good defense for the Arminian views of election. It's in the Scripture so they have to say something. Yet Arminians really seem to want salvation to be a result of our own decision to believe Christ. This means that God's election must be dependent on something. I'd affirm unconditional election, at least as some people would understand it. God has elected to atone for the sins of the world. Unlike the Arminian, I'd say this has nothing to do with my decision or inclination. Unlike the Calvinist, I'd say that we are able to reject God's election of us, and that without a continual working of the Holy Spirit we will indeed do so.
L - Limited Atonement - I know most Calvinists now prefer the term "particular atonement." By this the Calvinist says the death of Christ is effective only for the elect. He did not die for everyone's sins, but only for the sins of the elect. The Arminian will flat-out reject this idea. Arminians almost universally affirm that Christ died for everyone's sins. Calvinists will defend God's sovereignty by saying that his death is absolutely completely effective in every instance, therefore he died only for those who believe. Arminians will defend man's responsibility by saying that Christ's death is effective but we are able to reject the substitutionary atonement. I'd have to say there is more than adequate Scriptural evidence that we are able to thwart God's will, that Jesus is the one who takes away everyone's sins, and that we reject him.
I - Irresistible Grace - Most Calvinists now prefer the term "effectual call" but that really ruins the acrostic. Calvinists, defending God's sovereignty, affirm that when the Holy Spirit calls people, they cannot refuse. He gives people a new heart to believe and then calls them, so there is no way in the world anyone who is called will refuse. All who refuse the oral and written calls to repent and believe are, in fact, not of the elect, did not have Christ atone for their sins, and have not been called by the Holy Spirit. Arminians, on the other hand, will affirm God's grace shed on every person, that all are able to come to repentance and subsequently receive forgiveness. Both of these views fall short of a Scriptural understanding that God in fact uses real means of grace to impart saving and sustaining grace to people. The Scripture says that people receive regeneration of the Holy Spirit through hearing the Word, which imparts faith. People are baptized for remission of sins. People receive real forgiveness when God's word of absolution is proclaimed over them. People receive real spiritual nourishment when the literal body and blood of our Lord and Savior is given to them, consecrated by the words our Lord gave, saying "this IS my body." God uses means of grace and they accomplish their purpose, according to the promises given in Scripture. Yet when we choose to reject those means of grace, they become ineffectual. They are not resistible but they are rejectable.
P - Perseverance of the saints - Calvinists will affirm that all the elect live out their lives in the Christian faith. Those who depart from the faith were never believers to begin with. Those who seemingly believe on Christ, seem to depart from the faith, then return to faith in Christ were not true believers the first time or else were believers all along but spent some time not acting like believers. Arminians tend to go a very different tack with this. Because our salvation is mediated by our decision to believe, we believe and are saved, we reject and are rejected, we believe again and are saved again, etc. Of course, the vast majority of Arminians expect and hope that once someone believes that person will remain faithful to the end, as do Calvinists. Yet their views of the person's security are quite different from each other. The picture the Scripture paints isn't quite as mechanistic as either a Calvinist or Arminian view here. It is that those who are believing in Christ are believers. All who die in faith in Christ are redeemed. It doesn't seem appropriate to go beyond this, as the Scripture never seems to do so.
So this post has ended up saying why I'm not an Arminian and why I'm not a Calvinist. Ultimately both views seem to go beyond what the Scripture teaches in their attempts at systematizing the way salvation and persistence in the faith happen. Of course there are lots of places we could engage in dispute, as have countless others through the generations, about various specific points. But I won't push that right now. My point here is simply to lay out, in sketch, the most important distinctives and some of my reasons for rejection of each of those points of view.
So, come on, LPR people and other Lutherans who check this blog - fix me up and point out where I've run madly astray! All you Arminians and Calvinists are welcome to as well, just remember, everyone, do it in a kind spirit, remembering I've tried to be fair and charitable to your points of view as well.
The tea is still hot, kind of. Good night!