ה. וְעָנִיתָ וְאָמַרְתָּ לִפְנֵי יְ־הֹוָ־ה אֱלֹהֶיךָ אֲרַמִּי אֹבֵד אָבִי וַיֵּרֶד מִצְרַיְמָה וַיָּגָר שָׁם בִּמְתֵי מְעָט וַיְהִי שָׁם לְגוֹי גָּדוֹל עָצוּם וָרָב
5. And you shall call out and say before the Lord, your God, "An Aramean [sought to] destroy my forefather, and he went down to Egypt and sojourned there with a small number of people, and there, he became a great, mighty, and numerous nation.This commentators stat that the Aramean was Lavan and that he sought to destroy Yaakov and his family by integrating them into the idol worshiping society of his day. That is why Yaakov had to flee with his entire family. Lavan laid claim to the entire family and was only stopped by an explicit command of G0d.
When the famine occurred in כנען, Yaakov could have gone to his family, just as he had when fleeing Esav. However, he knew that the influence of Lavan and his sons would have completed the destruction of his family. That is why he had insisted on an oath that neither side would cross the boundary line that they had set up when he was returning to כנען.
THus, the sentence in effect reads that because the Aramean (Lavan) tried to destroy "our father" (Yaakov), he went down to Mitzrayim. It was there that he was able to establish the family and begin turning it into a "great nation".