I have been working on a little write up about the NO Offertory. I think that there's been a lot of emphasis placed on references to the Mass being a sacrifice being taken out of the NOM, but there are still in fact some that remain, especially in Eucharistic Prayer I (mostly the Tridentine Canon if you compare the Latin).
But I think that's the wrong emphasis, since "sacrifice" doesn't necessarily mean a sacrifice such as that of the Mass, as there are expressions like "sacrifice of praise", and the word itself just means to make holy and to dedicate something to God, setting it aside from the world.
When you get to the part of the Mass where the priest re-enacts as it were what Our Lord did at the Last Supper ... what is he actually doing? For all you know, he could just be re-enacting it, in the sense of doing it just to remember what He did, as a symbol of His sacrifice on the cross, as a so-called "institution narrative". So, that's where the Offertory becomes absolutely critical. It's in the Offertory where the Rite of the Church specifies ... "OK, in what follows, this is what we're doing." It actually disambiguates the meaning of what follows and sets the intention of the Rite.
In the Traditional Mass, the priest says we are offering the Spotless Victim (Hostia) for our sins. Now, some older translations say "Host", and I can't help but wonder whether that's deliberate. If you look up the Latin word, however, you'll find that Hostia is a technical term for a blood offering or vicitim in a sacrifice. Colloqually, however, the unconsecrated bread wafers have come to be called "Hosts", and with that "Host" translation, it may have been preparation for what was to come. Father Cekada's book Work of Human Hands does a great job showing how the liturgical revolution had been underway for a very long time before the NOM, to an extent that I had not been aware of.
So, the Tridentine Mass, the Offertory says that the priest is offering the Spotless Sacrificial Victim for our sins.
Father Cekada says that the NOM does not have an Offertory. Not quite. It certainly does not have anything that resembles the Tridentine version, but it definitely has an Offertory.
What does the NOM say we're offering? We're offering the "fruit of the earth" and "work of human hands", so they may become our spiritual food / drink. Uhm, so instead of offering the Spotless Victim, we're offering ... bread? wine? I doubt bread and wine will do anything to make satisfaction for our sins. But it gets worse. Some have pointed out that the NOM Offertory resembles a Jєωιѕн table prayer, and that it most certainly does. Marie-Julie Jahenny related a private revelation in which Our Lord told her that the enemies, the ones who crucified Him (= the Jews) were preparing a New Mass that would be "odious in [His] sight" and would contain "words from the abyss". So Jєωιѕн table prayer replacing the Offertory certainly would qualify.
Now, if you take a look at the sacrifices of Cain and Abel. Abel offered a spotless lamb (Spotless Victim) and his offering was accepted by God. Cain offered ... the "fruits of the earth" ... and God rejected it. Now ... think back on Adam's punishment for Original Sin. God told him that "cursed is the earth in thy work". So we have "fruits of the earth" offered by Cain, to which the Novus Ordo also adds "work of human hands", but God had cursed the earth in human work, the work of human hands. So ... the Novus Ordo Mass has the priest offering to God that which He in fact had cursed as a punishment for Original Sin. St. Paul said Cain's sacrifice was rejected due to lack of faith, but what does that mean, since Cain certainly believed in God. Well, it means that for some reason he paid no attention to the fact that God had cursed the fruits of the earth. God made this contrast as a way to foreshadow the difference between the Tridentine Mass, offering a Spotless Victim, just like Abel and the NOM, offering to God the "fruits of the earth", just like Cain, the "work of human hands", after God had CURSED the earth in our work. This also presages the fact that only a Spotless and Innocent Victim could make up for the sins committed against God, and not the cursed and Fallen.