Here's my 'long shot' take.
Frank has done the math. He knew a long time ago that Becca was conceived when he was with Shannon the first time, which either means that Shannon cheated, or Becca was his (or, I suppose, Becca was a preemie, but that assumes that Shannon got knocked up shortly after moving, and is not interesting narratively)
For a decade, his family dynamic relied on avoiding and ignoring that fact. It is habitual, but he has a tell. Searching through the game files for the line "you're my" reveals a lot of times when people state a relationship ("You're my sister", "You're my dewdrop", etc.). The only exceptions that I found where he didn't complete that sentence was in the lead up to sexy time with Becca. It could be that Frank calling Becca his daughter brings up more cognitive dissonance than equivalent lines with the other girls. Or I could be over thinking two lines.