It's all a matter of biblical interpretation.
Passover is a time for questions. Four come to mind immediately, but here's an important fifth: Will there be lamb at the Seder? The answer, as with so many other things in Judaism, depends on your family's traditions.
Ashkenazi Jews, those whose ancestors settled along the Rhine River and in Northern France (and eventually spread into Eastern Europe and Russia) typically do not eat lamb at Passover. According to Rabbi Batshir Torchio, Ashkenazi Jews liken eating lamb at Passover to eating the paschal sacrifice (or korban Pesach). Traditional lamb offerings were intended only for Temple sacrifice and since the Temple was destroyed, there is now no place for that sacrifice. Instead, Ashkenazi jews place the zoroah on the Passover table, which is the symbol of God’s outstretched arm lifting the jews out of slavery, and serve brisket, which we can all agree is a delicious alternative.
Sephardic jews, those whose ancestors settled in the Iberian peninsula prior to the Spanish Inquisition, often do eat lamb at Passover. According to Rabbi Torchio, "The Sephardic community interprets this differently as they are re-enacting that last evening before the Jews left Egypt, and are literally ingesting the narrative of the Exodus from Egypt toward becoming a nation." The one caveat being that while you can can eat lamb meat, you must not roast a whole lamb, per Jewish law.
There are other differences between Ashkenazi and Sephardic Passover practices as well, including the great chametz vs. kitniyot debate about which grains and legumes are acceptable for Seders. However, rather than try to get the two sides to come to a consensus, it seems only fitting to let them agree to disagree. It wouldn't be Passover without a little infighting, so why break from tradition?