Q: Are we Christians because we were born into a Christian family?

A: Let me first ask you questions: How do you explain the conversion of Paul? He came from a very strong Judaistic family/culture/education, how did he become Christian? How do you explain the conversion of Muslims - who had been born and grew up in Iran - into Christianity? We Christians believe that we are saved by grace alone. And nothing is impossible for God.

But perhaps this question came from a relativist, or a pluralist. S/he believes that all truths are the product of social conditions, that we are conditioned by our upbringings, our families, our cultures, and so on. Ok. If that’s the case, I would remind him/her that that belief itself is socially and culturally conditioned. S/he won't even ask that question if s/he was born in China, say 60 years ago. I agree that social conditionedness of our lives is a fact, but it can’t be used to argue that all truth is totally (or absolutely) relative. Because that very argument refutes itself. As Peter Berger says, "Relativity relativizes itself."

I suggest you read: Tim Keller, The Reason for God.