This goes back to an argument that was very popular in 19th century: "is person's character inborn or is it a result of upbringing?"...
What is meant by "rebirth" in Buddhism is rebirth of the state of mind. In modern terms we could say that the living brain is only a carrier. So where does our state of mind come from?
Once as I meditated, I realized that some of my typical thoughts came back from my childhood, from my parent's dysfunctional family situation. And the roots of that situation can be traced to my father's childhood, and probably beyond, to his father's life.
Not all of it is passed down the family lines either. Today at least some of my thoughts came from news I read online about the situation in Ukraine. Do you understand? Our state of mind at any moment consists of elements each of which came down a chain of interactions that can be traced back to beginningless times!
Our state of mind is not "one thing", not an entity, there is no "I". The boundary between inner and outer is a fiction; there is an infinite sea of interacting mental and physical factors.
So why call it rebirth then? Because of appropriation. We appropriate a combination of traits as "I", "me", "mine". My country, my family, my childhood, my education, my believe, my values, my principles, my pride etc. Appropriation of these causes rebirth and suffering.