It is true that all cows (including grass fed cows) do emit methane in their burps (which contributes to climate change).  However, it is our view that they have been unfairly blamed for the increase in methane levels around the world and replacing these fossil-fuel efficient animals that produce nutritious food with more fossil fuel use is not going to stop climate change. 
Methane is emitted from a wide range of sources. Much of it can now be seen from new satellite data to arise predominantly from fossil fuel industries themselves. Methane also comes from rice fields, melting permafrost (caused by rising temperatures due to long term  fossil fuel use and rising CO2) and landfills.  Methane emitted by ruminants grazing on pasture is naturally broken down by methanotrophs – bacteria which feed on methane and tend to live in habitats such as wetlands, soils and other aquatic systems.  The methane is part of the natural carbon cycle and is all recycled, lasting only about 12 years in the atmosphere.
On conventional farms (i.e. non organic), cattle and sheep are often put into barns, away from grass fields and fed on grains and other manufactured foods because that is more convenient and they can be fattened and managed more easily leading to cost efficiency. However, this sort of animal husbandry relies on fossil fuels causing more CO2 emissions.
Although it is important we do not increase methane production unnecessarily, pasture-fed ruminants play a significant role in providing us with nutritious protein and fat without necessitating much CO2 release in that they can eat grass – which is a perennial crop that grows with little intervention – particularly when the animal walks to the grass itself and artificial fertilisers are not used to increase grass growth.