I also think part of it is because by admitting to the problem and acknowledging the need for help you are bringing yourself dangerously close to having the substance taken away from you.
The primal need, even on an unconscious level, is to keep steady access to whatever it is you are addicted to. The thought of being without it is terrifying because you just don't think you can be without it without being really sick. So, in a weird convoluted way denial keeps you 'safe' - 'safe' as in no one will try to take your alcohol, drugs whatever away. Your too messed up on the alcohol and drugs to see or think clearly and understand that the reality is that everyone already knows without your telling them and getting out from under the addiction can't happen until you take that scary step of admitting it.
I'm only speaking from my own experience and of people I would talk to when in rehab. It could be very different for others