A new mishnah - checking back the lineage of a woman who marries a kohen, namely 4 women which equals 8, when you consider 4 generations on both sides. Though some families, who were in various kinds of public service, were exempt from some of those checks, because they wouldn't have been eligible for those roles if their lineage had been blemished. But why davka the women and not the men? Also, fights about lineage brought out the insults from others. Plus, the position that converts cannot be Jewish kings, with potentially painful implications for other roles of leadership as well. And recognition of how uneven treatment of converts were in different communities.