In 1 Cor 5:7-8, Paul says, “…Christ, our paschal Lamb, has been sacrificed. Let us, therefore, celebrate the festival…”
One thing about the Old Testament paschal lamb, which prefigured Jesus Christ, is that any Israelite who wished to receive the benefit of the paschal sacrifice had to eat of the lamb. (Exodus 12:8) Likewise, any Christian wishing to benefit from the sacrifice of our paschal Lamb, Jesus Christ, on the cross at Golgotha has to eat of him, eat his flesh and drink his blood. Jesus said this in John 6:51-58. At Mass, our paschal Lamb, Jesus Christ, becomes really present, under the appearance of bread and wine, so that we might eat of him and benefit from his sacrifice on the cross at Golgotha.
In 1 Cor 10:16-22, Paul draws a parallel between the people of Israel, pagans, and you (Christians) and speaks of partaking of the Eucharist, “the bread which we bless…the Body of Christ” and “the cup of blessing which we bless…the Blood of Christ”, in the context of eating food offered in sacrifice:
16The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ? 17Because there is one bread, we who are many are one body, for we all partake of the one bread. 18Consider the people of Israel; are not those who eat the sacrifices partners in the altar? 19What do I imply then? That food offered to idols is anything, or that an idol is anything? 20No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be partners with demons. 21You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons.