'We admitted we were powerless over alcohol—that our lives had become unmanageable.'
Generally, AA members suggest that these two ideas are quite separate, and that 'unmanageability' is your life being a mess externally or internally, setting aside the drink question.
This won't do. Remember: we are effectively defining alcoholism here. Any feature of Step One must be true for alcoholics but not for non-alcoholics (or at least true only of people with some sort of addiction). However, everyone on the planet has a degree of external or internal mess; the question is only one of degree. Under this reading, the Step seems badly phrased, because, without the degree of unmanageability being quantified, we are being asked to identify a feature we share with everyone. In addition, many people come into AA with external or internal lives that are actually way less messy than those of some long-term sober members of AA. Check out Jim's story (page 35 et seqq.) and Fred's story (page 39 et seqq.) of the book Alcoholics Anonymous. If being a mess externally or internally, setting aside the drink question, is required for admission of alcoholism, then neither qualify, many long-term sober members qualify more than some newcomers, and most non-alcoholics qualify.
So, we can safely conclude that this cannot be the intended reading.
Sometimes people suggest that unmanageability is our inability to influence certain factors that affect our lives. There are such factors, but this is no more true of alcoholics than non-alcoholics. We might as well say, 'We admitted we were powerless over alcohol—that we were carbon bipeds'.
Furthermore, the grammar suggests there was a time when we were not unmanageable but transitioned to unmanageability. The 'unmanageability = incompetence' and 'unmanageability = powerlessness over certain external factors' readings are inconsistent with this idea of transition as both were true before we became alcoholics.
A much more plausible reading stems from the book Twelve Steps and Twelve Traditions.
'It is a tremendous satisfaction to record that in the following years this changed. Alcoholics who still had their health, their families, their jobs, and even two cars in the garage, began to recognize their alcoholism. ... Since Step One requires an admission that our lives have become unmanageable, how could people such as these take this Step? ... By going back in our own drinking histories, we could show that years before we realized it we were out of control, that our drinking even then was no mere habit, that it was indeed the beginning of a fatal progression.'
Clearly: unmanageability has nothing to do with being ineffective in your life (or emotionally unstable): it is simply the entailment of being powerless over alcohol. If you cannot choose when and how much you drink, you are not in charge of your life.