Does God expect believers to grow in the Word?
Yes, God expects growth from His children. New believers start on milk and are not expected to immediately comprehend the deep things of God's Word, but growth is required. If a believer is not more steeped in the Word now than a year ago, both teacher and student have failed.
Les explains that the word carnal here refers to believers who have not come out of the fleshly experience and are still under the control of the Old Adam rather than the Holy Spirit. They are saved, in Christ, but weak spiritually, so Paul calls them babes and says he fed them with milk. Les has patience with new believers and does not expect them to suddenly comprehend all the deep things of God's Word, but he looks for growth. He tells his classes that if they are not more steeped in the Word now than a year ago, then he has failed and they have failed. God expects growth from His children. The Corinthians, though believers, born again, and placed into the Body of Christ, were still so steeped in the flesh and fleshly minded.