I believe that with palm oil the issue is that the entire tree is cut down as the oil is inside the core of the trunk. If people were soley using farmed trees, it wouldn't be so bad, but instead people are clearing animal habitats.
The oil is in the fruit of the tree not the trunk, they don't cut down the palms to extract the oil, they cut down the rainforest to make room for the palms. https://en.wikipedia.org/wiki/Palm_oil