IMO the only ancestry that matters is living ancestry. Now what's living ancestry changes depending on the circumstances. Nobles traced back their ancestries for centuries because it was tied with the state, or some kind of religious ancestry. Their ancestry went back centuries because the state also went back centuries, or this is what they wanted to imply. For landed elites ancestry usually went back as long as they lived in that land, or at least in that town, owning different pieces of land in that area. You don't have to abstract away an ancestry 7 generations back when you were born and grew up in the same land, maybe the same house, as those 7 generations back.
Now, one of the main traces of modernity is that we inherit little to nothing from our forebears. When it comes to ancestry, we are so atomized that we divide ourselves in generations, already from father to son. People find more kinship with people of their own generation than their own parents. Basically ancestry is dead at birth in modern families. There's only dead ancestry, and this is why when modern people want to talk about ancestry, it's always something abstract and already dead. Ancestry can be anything whatsoever.
>you can be anything you want
What your parents are really saying is that you won't inherit a trade, business or a profession from them. This is one of the best marks of generational break in modernity.