I cannot say for sure why the authors of the Big Book wrote that, but I can say why it is the number one offender, in my experience.
To be resentful is to look at reality and say: 'it should not be so'. The reason I feel it should not be so is that I have my own template for reality. Sometimes this is consciously formed; sometimes this is revealed for the first time by upset; but upset (whatever the form) always reflects the fact I have a plan.
In fact the more often I am upset, the more detailed the plan. If, wherever I go, whatever I do, I find myself upset, I might conclude that the plan seems to encompass every aspect of the universe.
Pride can be defined as 'putting self in the place of God as the centre and objective of our life, or of some department thereof. It is the refusal to recognize our status as creatures, dependent on God for our existence, and placed by him in a specific relationship to the rest of his creation'.
There is no more egregious way to put self in the place of God than to cast ourselves as the creators of the universe, complaining that the actual universe ain't matching our blueprint.
This means that, to the extent that I am resentful (frightened, threatened, angry, sore, burned up, etc.), to that precise extent am I putting myself in God's seat, and, in my conception, where is God then? Does not exist. For I have taken His place. Pretty chilling thought.
With such a grotesque usurpation of God's position, it is not hard to see why precisely this is the 'number one offender': I cannot have a relationship with God and play God at the same time; I cannot live my true life if I am engrossed in acting out another role; I cannot have relationships with other people if they are simply characters in my play.
In addition: when I attack others (which is essentially what resentment is: an attempt to manipulate the world through sheer force of negative thought), I invariably feel under attack myself. Whatever I give out, I am giving back to me, because I am you and you are me.
Furthermore: when I attack, I believe I am betraying (perhaps not consciously, but it is there), and I feel guilt. Ever been out with friends, gossiping about someone, then a fellow says something kind about the person in question, and everyone falls silent and guiltily stares at the table? The guilt was there all along: the restoration of true sight triggered by the kind observation reveals the sense of betrayal hidden beneath the anger.
Anger is always, therefore, associated with fear and guilt, and the picture of isolation is complete.
Resentment cuts me off from God, from my true self, and from others—hence from the sunlight of the spirit, and the whole array of acting-out options (drinking, using, controlling, sex, spending …) start to entice, to apparently heal this apparent rift.
When I am connected with God, with my true self, and with others, I am bathed in the sunlight of the spirit, and there is nothing to fix.
Here's the great news: I am not disconnected—it is an illusion residing solely in my mind; it is my mind that needs changing, not the world. I have not really separated myself from others; I am merely blinded by my own thinking. No one has abandoned me in truth; I have abandoned no one.
The remainder of Step Four and the remaining eight steps beyond Step Four heal my vision. The healing happens from the inside out but is activated by action.
As 'Pookie' from Austin once said: you've gotta take action to activate your faith—God ain't gonna slide no hot dog under your door.