How was Eve being Adam's complement related to Christ and the church?
Just as Eve was given to Adam as his complement and became part of him, the church is Christ’s complement and part of Him. Ephesians calls the church His body, with Christ as head; the head in heaven and body on earth cannot be separated, and marriage pictures Christ and the church.
Les explains that the Greek word for “fullness” in Ephesians 1:23 also means complement, so the church is the complement of the head. He connects this to Genesis, where Eve was given to Adam as his complement and became part of him. Then in Ephesians 5, Paul uses the physical marriage relationship between husband and wife as the beautiful picture of Christ and the church, which is His body. This illustrates the head/body relationship: the church has its head in heaven, the body is on earth, but they cannot be separated. Les also notes that Peter does not bring out anything like this and never mentions the body of Christ.