Weird, unexplained memory?

I for some reason have this memory that I could've sworn was real, but actually isn't.

When I was much younger, my father used to smoke cigarettes. I have this vivid memory of my father one day relaxing in the house, smoking a cigarette. I remember him wearing a green tank top and some shorts as he was smoking.

When I try to explain this to the rest of my family, they all say that it was impossible, because in reality, I wasn't even born yet, and that it was actually my older brother who remembers that, which makes me extremely confused.

If I wasn't even alive yet, then how come I remember that event happening so clearly as if it actually had happened?