There are a lot of environmental issues with vegetarianism and veganism. There is no doubt that Western society, especially North America, eats too much meat and that factory farming of livestock to keep up with such high demand results in unethical treatment of animals, as well as horrible consequences on the environment and for climate change. The problem is that the intensive farming of cash crops for a vegetable/grain-based diet is also very problematic. It reduces biodiversity, requires the use of horrific levels of pesticides and artificial fertilizers, and kills the soil. The only way to keep up intensive agriculture in both environmentally and economically sustainable ways is with mixed farming that requires the raising of lifestock for meat, cheese, eggs, etc. alongside the growing of plant-based produce. Here is a great article on the issue from an Ecosocialist blog:
Why avoiding meat won't save the planet
It's all about the old three-field crop rotation most of us learned about in elementary or high school. Crop fields need time off to rebuild the nutrients in the soil otherwise the soil becomes depleted and exhausted. They need to be left fallow. Unfortunately, leaving arable land completely fallow and unused is just not economically viable for most farmers. Farming is a high capital, low profit business. The classical answer going back millennia is to use the fallow field as pasture for livestock. The lifestock can feed over of the grass and clover that grows naturally during the fallow period and will re-enrich the soil naturally with their manure. Proper pastureland maintenance also requires hedgerows and bush or woodlot, which is necessary for wildlife, bees, and biodiversity, etc.
On top of that, the other issue with a purely vegetarian or vegan diet is that, as Lily mentioned, in order to get proper nutrition from it, you have to heavily supplement and eat a wide variety of different fruits, vegetables, grains. Unfortunately, despite your local supermarket having all of those items year-around, they do not grow year around and most of them do not grow locally. The wide selection of foods that vegans and vegetarians rely upon is a Western capitalist luxury. It requires the shipping of produce that is either not in season or not endemic to where some lives by ship, rail, plane, or truck across countries and continents. In other words, it uses a ton of fossil fuels and produces a lot of greenhouse gas. Moreover, as fossil fuels become more expensive or we are required to change to more expensive renewable energy sources such a globalized food supply will likely become prohibitively expensive and such a variety will not be accessible.
In short, for the majority of people, the best way to eat going forward in an ethical, sustainable, and environmentally-friendly manner is to eat less meat, but to continue to eat a mixed diet based around biodiverse heirloom crops and lifestock raised locally and which produce the least amount of greenhouse gas both during produce and getting from farm to table. Instead of eating 10 large meat portions during the week, sourced from cheap factory farming operations, save up and have one nice Sunday roast sourced from a local, ethical producer, etc. Not only does it taste great, but it is also healthier, better for the environment, and you are supporting small, local business over big agribusiness and corporations. It is probably one of the most significant ways that an individual consumer can use their individual purchasing power to support green initiatives.