Passover and Last Supper

Here's how one scholar resolves the apparent contradiction between John and the Synoptics on dating the crucifixion:

We must begin with what is (emphatically) clear in the narrative before moving to what is unclear. The biggest and most traditional "constant" in the exegetical equation is the assumed relation between the Last Supper and the Passover meal, especially in the Synoptic Gospels. In the Fourth Gospel, however, such a concept is entirely and intentionally foreign. While it is usually assumed that the Synoptics make the connection clear, this assumption finds no direct warrant from Scripture itself. 

It is really only Mk 14:12-16 that allows for the suggestion of a Passover meal connection, and even in this verse there is no exegetical demand to view the Lord's Supper as a Passover meal. A few reasons can be provided. First, the reference to the Passover-meal "preparations" in Mk 14:12 is made by the disciples, not Jesus. While Jesus does give them instructions for the preparation of a meal, he never once refers to the meal as a Passover meal; the disciples assume it is a Passover meal because of the approaching Passover Feast. Certainly the meals are theologically related, but they are also (and necessarily) distinct. This might be exactly what the text intends to depict in its implicitness, with the absence of a Passover lamb (because it was not a Passover meal) making the point explicit–Jesus was to be the Lamb (Jn 1:29). Even if the disciples thought it was a Passover-like meal (Mk 14:16), that does not mean that it was viewed as such by Jesus. For him this meal was instituting (proleptically) the new covenant in his blood.

Second, there is no reason to suggest that the time of the meal in Mk 14:12 is on Friday, for on the normal Jewish method of reckoning days this meal would be on the evening prior to the sacrifice preparations, since the Jewish day was normally understood to begin at sunset of the previous day (as Mark's Gospel makes clear in Mk 15:46). "In other words, he [Mark] was as clearly aware as John was that Jesus held his Passover meal not on the official day, but deliberately one day earlier" [France]. And similar to the Gospel of John, we would argue that such an adjustment was not merely out of historical necessity but also for very important theological reasons. 

Third, the statement by the narrator in Mk 14:2 that the Jewish authorities were seeking to kill Jesus "but not during the feast" for fear of the people's reaction, adds further support to the chronology depicted by John. Unless the Jewish authorities changed their mind (about which the reader was not made aware by the text), this rules out the possibility that Jesus was arrested on the evening when everyone else was participating in the official Passover meal. That is, by Mark's own account, Jesus had to be arrested on the previous evening before the actual day of the Passover.

Fourth, the Barabbas incident (vv39-40; cf. Mk 15:6-14) is best explained on John's chronology. The obvious premise of the Barabbas release–an amnesty or pardon granted to some Jewish prisoner at Passover–is that amnesty was given precisely so that this Jew, upon release, could take part in the Passover meal. The common Synoptic chronology that relates the Lord's Supper to the Passover meal is unable to explain the point of Barabbas's release, for the meal would have already been celebrated! The Barabbas incident only makes sense if the Passover meal had not yet occurred and if the Lord's Supper (as recored in the Synoptics) is not the Passover meal.

By making the Passover meal the implicit background for the Lord's Supper (per Mark) or Jesus's final meal with his disciples (per John), the Gospels transfer the theology of Passover and the old covenant (the lamb, the blood, the ceremony) to Jesus and the new covenant. This is why John (and the Synoptics) is so careful to connect the final meal of Jesus to the Passover but not define it as such. For this final meal was actually the first Lord's Supper, and the only one that would look forward and not back, situated between the "Passover" meals of both covenants so as to make Jesus the fulfillment and subject matter of them both. In several places the Gospel has employed the historical reality of the Jewish "Feasts" in order to highly the cosmological forces at work in the narrative (see comments on 10:22). The use of the Passover in John is no exception. E. Klink, John (Zondervan 2016), 758-60.