Did Peter teach that the church is the body of Christ?
No. The body-of-Christ truth is not found in Peter's writings; he does not mention the body of Christ. That revelation is presented in Ephesians, where the church is called His body, with its head in heaven and its members on earth, forming the complement of the head.
Les explains that Peter never brings out the truth of the church as the body of Christ; Peter does not mention the body of Christ at all. The body-of-Christ revelation is presented in Ephesians. In Ephesians 1:22-23, God put all things under Christ's feet and gave Him to be head over all things to the church, which is His body, the fullness of Him who fills all in all. The Greek word for fullness also means complement, so believers are the complement of the head. Just as Eve was given to Adam as his complement and became part of him, the church is joined to its head. Ephesians 5 uses the marriage relationship between husband and wife as a picture of Christ and the church which is His body. Les points this out to show that Peter does not bring anything like this out at all.