Well, this is not really true. Animal agriculture is more or less the same total GHG emissions as the whole transportation sector, and it's technically way easier to switch to a vegetarian diet than stopping people from moving or finding new technological avances. So why not start with the low hanging fruits?
My point is that food is the one thing that's globally almost evenly distributed part of economy. And even if we all change diet's, it wont safe anyone's climate, if the rest is catching up with "western" lifestyles at their current emmisions footprint. Pretty much anything else is easier to change technically, if it wasnt for lobbyism.
I grew up in GDR and still had livestock of our own, this not just about food ethics, but also diversity/robustness of food supply in any more fragile economy.