Shulchan Menachem. We are learning Chapter Reish Mem Alef, 241, discussing the custom of the zeroa on the Seder plate.
The Rebbe brings in the Haggadah that the zeroa—the piece placed on the keara to commemorate the Korban Pesach—is not eaten. In Chabad, where a chicken neck is used rather than a shank bone, the minhag is still the same: it is placed on the plate but not consumed.
The Rebbe explains that this is not only a custom, but serves a clear purpose—to ensure that it does not resemble the actual Korban Pesach. Since the zeroa represents the korban, we must create a clear distinction so that no one might think that we are eating a Korban Pesach today, which is only permitted in the Beis HaMikdash.
One might suggest that it would be sufficient not to eat it during the Seder itself, but to eat it afterward. However, the Rebbe explains why the minhag is not to eat it at all.
The Korban Pesach is unique among korbanos in that its primary purpose is to be eaten. As explained in the Gemara, the entire offering is centered around eating the meat. Therefore, by not eating the zeroa at all, we emphasize that this is not a Korban Pesach. If it were eaten—even later—it could still resemble the korban.
By completely refraining from eating it, we highlight the essential difference: the real Korban Pesach is defined by its consumption, whereas this is only a remembrance.
Practically, in the Chabad custom of using a chicken neck with minimal meat, this is less of a concern. However, for those who use a more substantial piece of meat, the same principle applies—the minhag is not to eat it at all.
Summary
The zeroa is not eaten to clearly distinguish it from the Korban Pesach, whose primary purpose was to be eaten. By refraining entirely, we emphasize that it is only a remembrance and not the actual korban.