We did so why can't they? I think they shouldn't because of global warming and what science tell us, but there should be some compensation given under the form of a tax to keep the forest alive, I don't think that would be ecological blackmail at all.
The biggest export of Brasil is soy beans (27 billion market) mostly to China - https://oec.world/en/visualize/tree_map/hs92/export/bra/show..., but of course its much more complicated then that.
The China demand has increased recently due to the US trade wars, so that plays a role too.
There are tens of different crops used for all sorts of products, like palm oil used in doughnuts, kids cereals etc.
For example, leather is exported to China, that produces clothes that are sold globally a lot of it to the west, but not only.
The Amazon basin has a huge concentration of cattle in the world (200 million heads), and is a huge exporter of soy beans (27 billion market).
Pasture land and cattle feed crops are the main driver of the deforestation, so reducing global meat comsumption is the only way to stop the economic incentive to tear down the rainforest.
Brasil by itself has no interest in tearing down the forest to feed their population, this level of agriculture is for exporting and for feeding a highly resource intensive and environmental impactful process: meat production.
Its a global problem, maybe threatening the trade deal with Brasil is an effective short term solution to put some brakes on at least some of the damage, but without a global change of common habits like eating too much meat, the deforestation is not going to slow down anytime soon, by the contrary.