Nope, that’s not how the definition of a tree works. Look at swednek’s definition in the comments: it is a woody trunk with branches. There are many other plants you could make toothpicks out of (e.g. that are woody) that aren’t trees. For example, shrubs and lianas.
Most are wrong then. If you can make toothpicks out of it, it’s a tree.
You can make toothpicks out of anything if you’re willing to find a hard bit in it that can be sharpened or whittled.
Holds up a chicken. Behold! A tree!
bones are trees? o_o
Nope, that’s not how the definition of a tree works. Look at swednek’s definition in the comments: it is a woody trunk with branches. There are many other plants you could make toothpicks out of (e.g. that are woody) that aren’t trees. For example, shrubs and lianas.