From Pope Benedict's homily of 2007:
It was on the eve of his Passion that Jesus together with his disciples celebrated this meal with its multiple meanings. This is the context in which we must understand the new Passover which he has given to us in the Blessed Eucharist.
There is an apparent discrepancy in the Evangelists' accounts, between John's Gospel on the one hand, and what on the other Mathew, Mark and Luke tell us.
According to John, Jesus died on the Cross at the very moment when the Passover lambs were being sacrificed in the temple. The death of Jesus and the sacrifice of the lambs coincided.
However, this means that he must have died the day before Easter and could not, therefore, have celebrated the Passover meal in person - this, at any rate, is how it appears.
According to the three Synoptic Gospels, the Last Supper of Jesus was instead a Passover meal into whose traditional form he integrated the innovation of the gift of his Body and Blood.
This contradiction seemed unsolvable until a few years ago. The majority of exegetes were of the opinion that John was reluctant to tell us the true historical date of Jesus' death, but rather chose a symbolic date to highlight the deeper truth: Jesus is the new, true Lamb who poured out his Blood for us all.
In the meantime, the discovery of the [Dead Sea] Scrolls at Qumran has led us to a possible and convincing solution which, although it is not yet accepted by everyone, is a highly plausible hypothesis. We can now say that John's account is historically precise.
Jesus truly shed his blood on the eve of Easter at the time of the immolation of the lambs.
In all likelihood, however, he celebrated the Passover with his disciples in accordance with the Qumran calendar, hence, at least one day earlier; he celebrated it without a lamb, like the Qumran community which did not recognize Herod's temple and was waiting for the new temple.
Consequently, Jesus celebrated the Passover without a lamb - no, not without a lamb: instead of the lamb he gave himself, his Body and his Blood. Thus, he anticipated his death in a manner consistent with his words: "No one takes [my life] from me, but I lay it down of my own accord" (Jn 10: 18).
At the time when he offered his Body and his Blood to the disciples, he was truly fulfilling this affirmation. He himself offered his own life. Only in this way did the ancient Passover acquire its true meaning.
In his Eucharistic catecheses, St John Chrysostom once wrote: Moses, what are you saying? Does the blood of a lamb purify men and women? Does it save them from death? How can the blood of an animal purify people, save people or have power over death? In fact, Chrysostom continues, the immolation of the lamb could be a merely symbolic act, hence, the expression of expectation and hope in One who could accomplish what the sacrifice of an animal was incapable of accomplishing.
The Lamb and Temple
Jesus celebrated the Passover without a lamb and without a temple; yet, not without a lamb and not without a temple. He himself was the awaited Lamb, the true Lamb, just as John the Baptist had foretold at the beginning of Jesus' public ministry: "Behold, the Lamb of God, who takes away the sin of the world!" (Jn 1: 29).
And he himself was the true Temple, the living Temple where God dwells and where we can encounter God and worship him. His Blood, the love of the One who is both Son of God and true man, one of us, is the Blood that can save. His love, that love in which he gave himself freely for us, is what saves us. The nostalgic, in a certain sense, ineffectual gesture which was the sacrifice of an innocent and perfect lamb, found a response in the One who for our sake became at the same time Lamb and Temple.
Thus, the Cross was at the centre of the new Passover of Jesus. From it came the new gift brought by him, and so it lives on for ever in the Blessed Eucharist in which, down the ages, we can celebrate the new Passover with the Apostles.
From Christ's Cross comes the gift. "No one takes [my life] from me, but I lay it down of my own accord". He now offers it to us.
The paschal haggada, the commemoration of God's saving action, has become a memorial of the Cross and Resurrection of Christ - a memorial that does not simply recall the past but attracts us within the presence of Christ's love.
Thus, the berakah, Israel's prayer of blessing and thanksgiving, has become our Eucharistic celebration in which the Lord blesses our gifts - the bread and wine - to give himself in them.
Let us pray to the Lord that he will help us to understand this marvellous mystery ever more profoundly, to love it more and more, and in it, to love the Lord himself ever more.
Let us pray that he will increasingly draw us to himself with Holy Communion. Let us pray that he will help us not to keep our life for ourselves but to give it to him and thus to work with him so that people may find life: the true life which can only come from the One who himself is the Way, the Truth and the Life. Amen.