BTDT, Have you ever been around a family that has adopted a child? The ones I've seen, it's no different than if the parents had been the biological parents, they love the child as much as if they had born the child themselves. And the adopted children I have seen, call their adopted mother or father, mom and dad.
I'm not going to judge your situation of you not calling your stepfather dad. Maybe he wasn't a good dad to you, maybe he didn't earn the title dad. And I totally understand your decision if that was the case.
But someone can have more than one dad. It's not a betrayal of the biological dad, no matter how good of a dad he was, to call a stepfather dad, if he earns that title.
My opinion on that at least. It may be hogwash. :)
When Refreshed is talking about family, she means what the scriptures talk about, which I know you don't care about, maybe you throw those out as irrelevant to you, but nevertheless, all children of God, are a family, and are to love one another. My family in Christ is way more important to me than my blood family. Much of my blood family, I consider my enemies, although I still need to love them, as the scriptures say, love your enemies.