People don’t realise that herbivorous animals (who are naturally raised on grassy pastures) cycle carbon and fertilise the soil, helping to increase biodiversity and environmental health.
When properly farmed, livestock actually inject life back into tired soils and reinvigorate it. They can also help tackle the huge loss of biodiversity now found on most non organic farms due to their use of chemicals such as pesticides and fertilisers.
In addition, all the carbon that  livestock produce has actually come from the carbon dioxide in the air which has been captured by plants (during photosynthesis) and turned into sugars which are used by plants. Some of the carbon made by plants is also pumped into the soil in exchange for the nutrients the plant needs from the soil life and some of the carbon in the plants is eaten by the cow.
Well-managed, periodic grazing actually stimulates extra plant growth and therefore photosynthesis. Thus, grazing livestock can increase carbon levels in the soil, leading to greater carbon capture, often in stable carbon compounds that can be stored in the soil for a very long time. In this way, the carbon is locked up and the soil acts as a carbon sink. In contrast, fossil fuel use is a one-way process causing release of CO2 which is a gas that lasts for hundreds of years in the atmosphere.