If drinking less isn’t actually your priority at the moment, it shouldnt be the focus of your therapy sessions. And if your therapist doesn’t follow your lead, then you should get a different one.
If you find opening up and admitting shit in therapy hard, then make that your new focus in sessions. As someone who’s seen my fair share of therapists, most of them are very thankful if you start with “I almost didn’t come to therapy, because I kinda don’t belive it works” (but maybe it’s also that I feel hopeless about changing my life in general) or “I often lie in therapy because I want you to like me” (does that pattern appear in other parts of your life?)
Start with first obstacle, not the biggest or even the most harmful. Then you can work on those things first, rather than waste time, money and frustration pretending to be doing something else.
Yeah, when life wasn’t going well I’d sometimes buy a lottery ticket just to indulge in a fantasy of what would happen if I won. But then I’d find myself focusing on what would happen if I died and how I’d write my will…