The reason this is a question is because Step Two talks about restoration to sanity, which presupposes we are insane. What is the nature of that insanity, and what does it have to do with alcoholism?
Step One is about powerlessness over alcohol. That means I drink way too much when I drink and get horrible consequences, but I am also crazy enough to have the first drink in the first place, despite the years of consequences behind me and despite any prior resolve to remain sober.
It should be noted, however, that Step One on page 59 ('We admitted we were powerless over alcohol—that our lives had become unmanageable.') is merely a summarising line. The book 'Alcoholics Anonymous' goes to great lengths to explain Step One, in fact over many chapters. To understand Step One, this material must be examined; the Step cannot be simply 'read off the wall'.
I propose that the 'mental obsession' discussed in the book is the insanity presupposed in Step Two.
Here is a definition of the mental obsession:
'The idea that somehow, someday he will control and enjoy his drinking is the great obsession of every abnormal drinker. The persistence of this illusion is astonishing.' (Page 30)
Here, the mental obsession is referred to as an illusion. There is also reference to 'delusion' (page 30). But the most common characterisation of this phenomenon is that of insanity.
Page 37 (which is part of the Step One material of the book) makes clear this insanity:
'But there was always the curious mental phenomenon that parallel with our sound reasoning there inevitably ran some insanely trivial excuse for taking the first drink. Our sound reasoning failed to hold us in check. The insane idea won out. ... But even in this type of beginning we are obliged to admit that our justification for a spree was insanely insufficient in the light of what always happened.' (Page 37)
That's three references to insanity in one passage.
Here are some more:
'Then came the insidious insanity of that first drink, and on Armistice Day 1934, I was off again.' (Page 8)'Whatever the precise definition of the word may be, we call this plain insanity. How can such a lack of proportion, of the ability to think straight, be called anything else?' (Page 37)'However intelligent we may have been in other respects, where alcohol has been involved, we have been strangely insane. It’s strong language—but isn’t it true?' (Page 38)'I rather appreciated your ideas about the subtle insanity which precedes the first drink, but I was confident it could not happen to me after what I had learned.' (Page 40)'But with the alcoholic, whose hope is the maintenance and growth of a spiritual experience, this business of resentment is infinitely grave. We found that it is fatal. For when harboring such feelings we shut ourselves off from the sunlight of the Spirit. The insanity of alcohol returns and we drink again. And with us, to drink is to die.' (Page 66: note that the insanity, here, precedes the first drink.)'... those insanely trivial excuses to drink.' (Page 120)'He was on thin ice. Again it was the old, insidious insanity—that first drink.' (Page 154)
What does not help matters is that the word 'insanity' is also used to denote two other phenomena: how insane we are or appear when drinking or the insanity of late-stage alcoholism:
'Rumor had it that he had been committed for alcoholic insanity.' (Page 9)'He is seldom mildly intoxicated. He is always more or less insanely drunk.' (Page 21)'The persistence of this illusion is astonishing. Many pursue it into the gates of insanity or death.' (Page 30)'Sometimes there were screaming delirium and insanity.' (Page 107)'He is violent, or appears definitely insane when drunk.' (Page 110)
These references are to be distinguished from the insanity of the first drink, however, as elaborated upon above.
Thus, insanity is a key idea of Step One.