I know what you are thinking. This dude has fallen off of his rocker and landed on his head incurring massive trauma to his brain. Life and death are intrinsic opposites. But, on spiritual terms, let us rethink this oxymoron.
I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
The Apostle Paul here addresses what it means for a person to be alive and yet dead. As humans, we were made in the image of God (Genesis 1:27) meaning that we too are triune beings. Just as God reveals himself as the Father, the Son, and the Holy Spirit, so He created man with a body, soul, and a spirit. When we accept Jesus as our Savior, He saves our spirit not our soul. Our soul is the part of us that strives against God via the sinful nature that we all struggle with. That is the part that Paul is saying saying is crucified with Christ on the cross. That old, sinful nature needs to be put to death. You may ask why must this happen? I'm glad you asked. This must happen because the Scriptures make it very clear that no man can serve two masters. (Matthew 6:24) Jesus cannot live in a heart that has not been given completely to Him, and let's just be real here for a minute. Should He?
Moving on to the part we all like...the part where we are ALIVE. Once we have put our will, emotions, and minds to death, then God steps in and breathes new life into us! (II Corinthians 5:17) Then, like a butterfly emerging from a cocoon, the world can see our beauty!