I tend to agree with FG. What would be the point of his saying anything, if he knows deep down that he's not ready to quit, and that living with him is bad for you and the kids? He may care very much, but also realize it's for the best.
Alcoholism is very, very powerful. It's not as simple as "you or the bottle"--if you understood how utterly TRAPPED most alcoholics feel, you'd know that it's not a simple question of whether he loves/cares about you. Maybe someday he will have that moment of clarity and do what he needs to do. Nobody really knows when/if that will happen, or why.
As much as you think you wish he would "fight for" your marriage and family, if he's not THERE yet, it would only prolong the misery as he makes promises and token gestures, only to repeatedly fail. That does a lot more damage to everyone, in the long run, than allowing you to leave without a fight.