The argument for that position generally flows from the OT - how in Numbers 30 the father has the authority to void vows made by their daughters.
The summary of that position is that, "sons leave, and daughters are given." A son leaving his home and setting up a new household as he marries someone else's daughter, who is given by her father.
It's interesting that this picture isn't entirely what the OT puts forth. Abraham was still the head of his household, even after his sons got married and had children. It was Abraham and his whole household throughout. What did Isaac do upon his marriage? He doesn't leave his family structure to start his own, but he brings his wife into his mother's tent (Gen 24:67).
Just a random thought.