Food production systems such as organic agriculture and grass-fed beef have been proposed as potential ways to reduce agriculture's environmental impacts (e.g. Ponisio et al 2014). Organic agriculture, for example, is often promoted as having lower environmental impacts relative to high-input conventional systems because it replaces agrochemical inputs with natural inputs such as manure or with ecosystem services such as pest control (Azadi et al 2011).
I must say that I also think (thought..?..) that organic or grass-fed agriculture was better for our environment because less chemicals are used. But I do see there are many other factors that come into play after reading this article. Personally, my main drive in buying organic or grass fed, or pasture raised, etc is for personal health reasons as well. In my household I am a stickler when it comes to food quality. I try to buy in season, local and organic. We purchase minimal meat...but if we do we always go to a market where we can get the best quality. I have to admit, my thought process on that hasn't been for environmental reasons it has definitely been for health reasons. It may be more expensive to purchase, but to me it is one of the most important factors in life where I can "put my money where my mouth is" for the most important asset in life, my health.