Taken in its religious context I can see how this story would have appalled you as a child. In that context it still appalls me, mostly for the message to beautiful and innocent young children that for this reason they are born fallen and damned.

Taken in a purely allegorical context however the story makes much more sense. At some point in time our intelligence evolved to the point that we could understand the consequences of our behavior, the effect our own selfish or thoughtless acts had on others; we literally gained the knowledge of good and evil.

Around that point in time we became aware of the inevitability of our own death, a knowledge almost certainly denied to animals with less self awareness. Those events came paired to humanity, the knowledge of good and evil and the knowledge of our own deaths...on that day we certainly did die.