I’d say, it depends. As with any relationship, there’s some degree of compromise that should be taken, and any time one just refuses to put something on the table, either they’re being unreasonable, or it is important enough that it is something that one should end a relationship over if they can’t come to an agreement.
Further, I would make the argument that one has an alcohol problem not only if one is unwilling to give it up, but also if one actually does, that one can’t have even one drink without fear of losing control again. That is, the inability to drink in moderation, or can’t even have one or two drinks socially, then alcohol still has a grip on someone. That said, I would certainly say the latter problem is a better problem to have than the former, but it’s still an issue.
So, for him, how much fun is this drinking to him? How much would he care if he cut back or stopped or if other interests or obligations interfered with it? What about health issues? Chances are, if he’s drinking enough that he really shouldn’t drive, there may be some problems that come with it. Being aware that his girlfriend has issues with it, is he willing to compromise on it to make her feel better?
And for her, how confident is she in his ability to control his drinking? If she hasn’t seen any real issues yet, why can’t she extend trust to him to continue drinking but establish some sort of guidelines about how to identify when they think an issue may have arisen? If she is going to drink some, then she’d be a hypocrite to expect him not to drink, so what level does she expect him to pull back to?
From my experience, I’ll have a drink or two socially, but I find anything beyond a slight buzz to be generally unpleasant, so it’s very rare I’ll do more than that. That said, there was a girl I had a date with a few months back, she didn’t seem the type to drink in excess, but it did seem she would have drinks several nights a week. She talked about the drinks she enjoyed as part of the conversation, and she even works in the industry. She seemed great in all other respects, but as it turned out, even though she only rarely got drunk, it still came off as a dependence on alcohol, and it was enough of a turn-off that I didn’t call her back. So, at least for me, I do think there’s levels of problems with alcohol that are below drinking to excess regularly.
And I voted other, because I don’t think the answer is that he should flatly stop just because she asked. I think they should talk and figure out something in between that let’s him have some fun with his friends and lets her feel confident that he’s not going to deteriorate.