This came up in a discussion with 2 students (B and N, if you ever read this, it's you) and evolved into quite the thesis. It pertains to "Yachatz" of the Pesach Seder, its origins and purpose. Since Adar is around the corner, it's not quite too early to begin a discussion of Pesach.
First, some observations and 'clues' to help us along:
1) "Ha Lachma Anya", which immediately succeeds the breaking of the middle matzah, is part of 'yachatz', not maggid. it uses the definite article "THIS is the bread of affliction".
2) The paragraph of 'Ha Lachma Anya' was written in Babylonia - it's in Aramaic and explicitly states "This year we're here; next year in Israel".
3) In Temple times, it would not have been possible to extend an invitation at the beginning of the Seder, as the Paschal sacrifice required participation to begin much earlier, prior to the actual slaughtering of the lamb. it's only outside of Israel, or after the destruction of the Temple, that the invitation expressed in "Ha Lachma Anya" could work.
Here's where we get more speculative. The Afikoman as we know it is not mentioned in the Mishna. The Mishna states that one may not eat 'Afikoman' = 'dessert' after partaking of the Paschal lamb. Nowaday, we use Matzah instead of lamb chops for this final course. Thus, our eating of the 'afikoman' replaces the eating of the Korban Pesach.
If so, then perhaps we can take the afikoman/korban pesach connection further:
One can invite people to participate in the seder up until the point that the afikoman is designated. Thus, 'yachatz' is the last point until which anyone can join the seder!
And then we can suggest, perhaps, that the breaking of the matzah of the afikoman is a symbolic slaughtering of the korban pesach. I would marshall 2 bits of evidence for this:
1) The Gemara in Avodah Zarah discusses 'Toldot' - offshoots - of the central types of worship, namely, prostration, libation, animal sacrifice, and incense-burning. Amongst the 'offshoots' of sacrifice is breaking a stick in half as a form of worship. Thus, there is precedent for the notion of breaking something in half as a simulation of animal sacrifice.
2) One of the oldest and most bizarre Christian (specifically Catholic) accusations against the Jews was that they symbolically re-commit deicide by stabbing the wafer. given that the wafer derives its origins from the matzah of the pesach seder, that Passover symbolism has become a central part of Christian doctrine, including reference to Jesus as the 'Lamb of God', and that he was the sacrifice to end all sacrifices.
It stands to reason that the Jewish practice of symbolically slaughtering the Paschal Lamb by breaking a matzah would have been misunderstood as an anti-Christological performance.