Limited Atonement or Not?

Recently I've been studying the area of my theology that I really struggled with when I became reformed. This was probably the biggest sticking point that differentiated my theology from those in the reformed world. Limited atonement is probably one of the most hated parts of reformed theology by those who are not. What is the definition of limited atonement?

Limited Atonement: Christ died for and paid for the sins of the elect...He did not pay for the sins of every human being.

Now even the Arminians limite the atonement...unless you are a universalist and believe that everyone goes to heaven, you are limiting the atonement. The big difference would be that in the reformed world we believe God is sovereign and limits the atonement...in the Arminian world people assert man's sovereignty and say that man limits the atonement. The reformed view says that Christ's atonement was actual (actually paid for the sins of His intended recipients) and the Arminians says the atonement if potential (waiting for someone to believe and receive).

In my studies this morning I saw a passage that I'd not seen before and wanted to share it with you. Turn to John 10, 11-15:

Notice that in John 10:11 Christ Jesus says He died for the sheep- "I am the good shepherd: the good shepherd giveth his life for the sheep"

Notice that he repeats this in verse 14-15- "I am the good shepherd, and know my sheep, and am known of mine. 15 As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep."

In the following verses people get upset with Him and accuse him of having a devil and demanding that He declare His messiahship. Notice carefully what He says in verses 25-27:

"Jesus answered them, I told you, and ye believed not: the works that I do in my Father's name, they bear witness of me. 26 But ye believe not, because ye are not of my sheep, as I said unto you. 27 My sheep hear my voice, and I know them, and they follow me:"

Why don't the accusers believe in Him? BECAUSE THEY WERE NOT HIS SHEEP! This is so crystal clear to me...there are sheep and there are goats. Christ died for the sheep (those that believe)...but He didn't die for those who are not sheep. These people didn't believe BECAUSE they were not sheep.

Sounds like limited atonement to me.