When Paul wrote to the Christians in Ephesus, the city was second in importance only to Rome. At that time the Greeks and the Romans held a very high opinion of themselves as warriors, athletes and intellectuals. There was a stone image to the goddess Nike in Ephesus - the winged goddess of victory, both in war and in peaceful competition. There were three gymnasiums in Ephesus - which may say something about their priorities in life.
The point is that the Christians in Ephesus were more concerned with being members of the body of Christ, the church. Just as Christ loves those who belong to him, so too were the Christians in Ephesus to take care of one another as an expression of the love and care within the church.
As Paul said elsewhere, Christians belong to Jesus Christ (Romans 1:6; 7:4). They have been purchased with the blood of Christ (Hebrews 9:12).
To all who belong to Jesus Christ, they have the experience of being loved by God and of having everything to live for. Their lives have purpose and direction. Therefore they care for and nurture their bodies because they are living, not for self, but for others.