Estrogen dominance somehow went to a paleo theme on this thread if you ask me. Nothing wrong with it, but it doesn't answer the thread's question.
My understanding of estrogen dominance comes from a slightly different perspective, which the paleo/no dairy/clean carbs theme does address. The simple way to think about it comes down to asking what these things (modern dairy, bad carbs, etc) tend to do to the body, and in short, it adds on body fat. While we need a level of body fat in general (the brain runs mostly on carbs (ketones as well), but the heart runs on fats), we can all agree that excess fat is a problem.
The question is "why is excess fat a problem?" The answer: it's an endocrine organ!! And as such, it creates hormones!! Think about thin females who go thru menopause: what changes in their body shape shortly afterwards? They get a slight 'pooch' over their abdominal area. Their ovaries have shut down, but they still need a level of estrogen, which is supplanted by this deposit of fat, which continues to provide them with a level of estrogen.
The problem is men don't need that much estrogen, and invariably we see men with an excess of belly fat!! Men need testosterone to be healthy (Mike Mahler recently had an interesting podcast on this subject...if you can get past the childish joking around in the first 15 minutes, it's worth the listen). So the key comes down to balancing your hormones and getting those checked out thoroughly. Aside from Mahler, I haven't come across a lot of people talking about testosterone/male hormones in a meaningful way. But I think there's more going on with being a healthy male, and it largely involves getting hormones balanced out.