This is a myth. If you get blackout drunk and don't remember the night before, does that mean you ceased to exist in that time period? How can you prove any conclusion you come to?
The idea that being dead is the same as not being born seems like an elegant conclusion until you consider how much our perception of time varies even while we're alive, and it's actually an observation made after you gained your current consciousness; meaning that you truthfully have no idea what happened before you were born, only your current perception of it. What you're really saying is "I don't remember, and no one else remembers, therefore there was nothing".
Reality is unintuitive. Modern theoretical physics suggests that time itself is an illusion and that every state of the universe is superimposed into one unifying entity: past, present, and future. What does that mean about our perceptions of life and death?
The truth is we don't know much of anything, we can only speculate about it.