If you face you are an addict, you will deal better with it and achieve cure faster. So, why do people deny they are addicted to something?
First, nobody likes feeling helpless and out-of-control, maybe that's way they use, unconsciously, this defense mechanism. People "use" different kinds of this defense mechanism such as: supression, projection, rationalization, minimizing and etc.
Second, it is easier to blame someone or something else for our own faults, because we want to look good even if other people will not.
And last but not least, it is difficult to show we have problems and many people just realize that when they have already "lost" their families, jobs and friends. And that's when they ask for help, but other people take longer as they can't stop using the mechanism and try to convince others that their problem is not as bad as it looks.
Therefore, these are some of the reasons we will not admit being addicts and ask for treatment.