Based on several sources (Hank Jones, other Teator researchers), it appears the parents of the immigrants were Hans and Elisabetha Dather/Thater/Dother/Dotter.
They had three children: Lorentz, Georg and Margaretha. The whereabouts and/or life of Margaretha in America has not been ascertained.
Lorentz had one son Henrich who had Anna Margaretha, Johannes, Zacharias, Elisabetha, Catharina, Abraham, Henrich, Catharina (a second one!), Wilhelmus, and Philip. Most of these grandchildren married, and that's the reason for the genealogy.
George had nine children: 1-Maria Magdalena; 2- Johannes who had children with two wives: Georg, Johannes, Catharina, Sophia, Anna Maria, Johannes, Elisabetha, Philipus, Henrich, Magdalena; 3-Anna Elisabetha; 4-Anna Barbara; 5- Henrich who had children: Anna Maria, Rebecca, Georg, Beeltje, Johannes, Johann Henrich, Elisabetha; 6-Johann Friederich who had children: Anna Maria, Elisabetha, Catharina, Anna, Friederich, Georg, Jeremias; 7- Elisabetha; 8-Anna Maria; and 9-Lorentz. And most of these grandchildren married, even more reasons for the genealogy.
If you suspect that several names appear frequently, you are right. Keeping Johannes, Henrich, Friederich, and George, in addition to Catharina, Elisabetha, and Anna (and forms thereof) straight is a challenging task for the family historian. As difficult as it is to place people in the correct family, if it were not for church records and the work of transcribers like Art and Nancy Kelly, it would be almost impossible.