I can understand the difficulty in admitting "I am an alcoholic". It was difficult enough for me to admit to myself "my husband is an alcoholic" the first time, let alone say it aloud to someone. But after a while with repetition it gets much easier.
My husband was a social drinker when we married. ---> I see now he was already an alcoholic
Later he became a heavy drinker ---> an alcoholic
Now he's an alcohol abuser ---> still an alcoholic
To paraphrase Willie, a skunk by any other name still stinks.