Jonathan,

What William is saying is that if Jesus died for every person without exception, then Jesus is a failure because people He supposedly satisfied the wrath of God for are in Hell. Either you have to deny substitutionary atonement, believe everyone is saved, or believe Christ died for the elect (not that the elect never were lost, for the Bible says they once were lost).

Both Calvinists and Arminians believe in a limited atonement. It's just that the Arminians view it as limited in power, while Calvinists view it as limited in extent.

BTW, this thread is going off topic in my opinion, and we have discussed the atonement many places elsewhere on this board, which I'd encourage you to read. Also, here are several links to articles:

The Atonement of the Lord Christ

Atonement

Reformed Apologetics

True godliness is a sincere feeling which loves God as Father as much as it fears and reverences Him as Lord, embraces His righteousness, and dreads offending Him worse than death~ Calvin