Characters
That's my family, Kay. It's not me.
— Michael Corleone • The Godfather

Behind the line May contain spoilers.
Our reading
An editorial interpretation.
The speaker draws a boundary between personal identity and family identity, telling Kay that one should not stand for the other. The insistence asks the listener to judge the speaker separately. It can function as reassurance or self-distancing, depending on what prompted the comparison.
Context reviewed