How would I edit this image?

When you use the fuzzy select tool your selection must be a closed space. That is the easiest method here so I won't change it. On the left hand side of the tree you have an open space. Around maybe 8:30 er 45. If you close that lil line then you can remove the white on the outside of the tree without disturbing anything inside the tree. I did try it and it worked fine. I also lowered the threshold to zero. Since it is black and white that can be at zero. Think about the wand like a Roomba. The automatic vacuum. It will keep on going and selecting (vacuuming) up the pixels(dirt) until it hits a wall. Well it didn't have a wall on a teeny tiny part of the left hand side so it kept going inside of the tree.