One reason for brogramming is that our society (not everyone, but overall in various peer groups or subcultures) provides substantial social rewards for men who:

  - like sex
  - like beer and other alcohol
  - like to party
  - are "fun"
  - like to "hang out", "socialize", etc
  - various other stuff kind of along these lines (it's really not my scene, hard to give good examples)
  - demonstrate their strong commitment to these things. roughly: the more dedicated, the larger the social rewards.

So, brogramming is stupid overtly, and causes some problems, but if you tell people to just stop, a lot of them aren't going to want to. They may not know how to explain why, but one of the reasons is that brogramming provides them social rewards (ones that programmers in general are a bit starved for compared with athletes or even chefs).

You want social change? It needs to be broader. Brogramming is a symptom of something much larger. It's basically a coping mechanism for lonely people.

The most important driver of societal shifts are good ideas. Really high quality ideas. One type of idea that will help is changes that make things better for some and don't create any losers. Those are pretty easy to get everyone to agree to and like. But they are hard to come up with. They require a really good understanding of the situation and incentives and how people benefit from the behaviors you want them to stop (which normally gets into even more complicated, larger social structures, which normally touch on sensitive issues affecting most people).

I might be inclined to try starting somewhere else entirely if I wanted a large scale societal change. For example a lot of people feel shame regarding being alone. There are problems with being alone, plus social costs, but then there is this extra emotional cost that isn't from any actual concrete problem and even goes beyond the social costs. Help people be more proud of living alone and spending time alone, and feel good about it instead of bad, and that will be a step towards changing romantic relationship dynamics. Making standard romantic relationships a little more optional will enable people to question them a little more. And, very indirectly, that is a step towards less sexism or brogramming.