When we partake of the cup and the bread we partake in the nature of the Lord. To share in the symbols of His sacrifice is to identify with the God who sacrifices.
This is one of the reasons why Paul forbids idolatry before he gives instructions about communion in 1 Corinthians 10. Many of the Jews were idolators and he warns the believers to “flee idolatry” (verse 14). Behind idols are demons and “you cannot partake of the table of the Lord and the table of demons” (verse 21). Be careful to choose the right table.
When we eat the bread we participate in the body of Christ. We worship one who gave His physical life for us and we learn how to do the same. When we drink the cup of blessing we participate in the blood of Christ. We identify with dying to bring life.
This is how it must be. We either serve demanding idols and become demanding of others or we serve the God who gives grace and become merciful. We either identify with false gods who consume or we identify with the true God who was crucified for others. “Those who eat the sacrifices [are] participants in the altar” (verse 18).
Our sacrifices are not original. We cannot save another man’s soul. But we can imitate the ultimate sacrifice. The lesson is on the Table before us.