The removal of trees to allow the land to be used for other purposes (such as the growing of arable crops or pasture) has been taking place for many thousands of years, with steady removal going on in Europe and the US over the last few hundred years.
However, it is the extremely rapid destruction of mature tropical rain forests that is now causing such concern. It is estimated that about half of the tropical rainforests that once existed have gone, with the greatest loss in Southeast Asia. Now, massive areas are being lost in central and south America, Indonesia, Nigeria and other parts of Africa.
In the past, slash and burn by shifting cultivators was often done on a small enough scale to be sustainable because the forest could recover; but now massive areas are cleared and the nutrient-poor soils quickly become exhausted and eroded after just a few years of arable cropping. Often the local climate is affected, causing damage to the remaining forest.
So far as Peak Food goes, deforestation is a major cause of the enhanced greenhouse effect as the decay and burning of wood releases stored carbon back to the atmosphere. We are now seeing droughts and floods reducing crop production in various parts of the world.
But the use of these forests is not adding much to food production. Besides the fact that in many cases the land is often abandoned after the nutrients have been used up, much rainforest is now being destroyed not to produce food but for biofuel. Many millions of acres are going into oil palm for biodiesel or sugar cane for ethenol. These products are coming to Europe to help in the reduction of CO2 emissions, but some experts say that these fuels will never reduce emissions enough to make up for the emissions produced when the forests were burnt.