The main driver of deforestation has always been the expansion of farmland. A recent study published in Nature Food by Chandrakant Singh and Martin Persson shows which products, specifically, have driven the process in recent decades. The clear leader was beef production, which accounted for 41% of total deforestation. Second came oilseeds (mainly soy and palm oil), followed by artificial forest plantations and cereals.
The forest loss is tightly tied to specific regions. More than half of the clearing for pasture happened in Brazil and its Latin American neighbors, while almost all the world's demand for palm oil is met at the expense of the forests of Indonesia and Malaysia. Forest plantations became the main factor in the US, Canada, China and other parts of Asia, whereas in Africa the chief culprits of loss were cereals, roots and tubers, and cash crops like coffee, cocoa, fruits and nuts.
The scale of the problem is hard to grasp, yet the data shows that change is real. In places, international campaigns and regulation have worked, for instance, the pace of clearing for palm oil in Southeast Asia has been slowed. But to pull off the same trick with the rest of the agricultural sector, we'll have to pin down exactly which capital, and at which precise points on the planet, is putting forest to the blade.
I rarely do, and when I do is Danish beef (I am in the EU). That said, that is not at all what you should get from the article. You should not buy Latin American beef, and you should consume way less chocolate, coffee, and fruits and nuts that are not in season and/or local.
Switching to tea (good tea, not the bagged shit), is probably my biggest contribution to saving the planet, since the environmental impact is less than a third of the coffee production both in terms of energy, fuel for transport per portion and water consumption for the crops.