Think about the stigma that is attached to the idea that alcoholism is a disease, an incurable illness, and you have it. That's a terrible thing to inflict on someone. Labeling alcoholism as a disease, a cause unto itself, simply no longer fits with what we know today about its causes.
To give up power to change for the better is inherently distasteful to everyone, and to force people to affirm that they are addicts or alcoholics so they can speak in a meeting is shameful and demoralizing.
AA purports to be open to anyone, as it is stated in Tradition Tree, "The only requirement for AA membership is a desire to stop drinking," but it isn't open to everyone. It's open only to those who are willing to publicly declare themselves to be alcoholics or addicts and who are willing to give up their inherent right of independence by declaring themselves powerless over addictive drugs and alcohol, as stated in Step One, "We admitted we are powerless over alcohol- that our lives had become unmanageable.
How do you think your body and mind would respond if you were surrounded by psychologists, psychiatrists, or drug and alcohol counselors who subscribed to the belief that "once an alcoholic or addict, always an alcoholic or addict" and who believed that your current stay in rehab would be one of many?