Question

Explain why treehouses dont change in height as a tree grows

Answer 1

Treehouses are built on the stem and the three branches, which do not grow in length, only in width. Trees grow in length only in the area of the buds, which are located at the ends of branches. 
Maybe it is easier to understand this if you imagine that you put a small house replica on the palm of your hand and that your fingers are constantly growing from their tips.  So, the house on your palm would not move, only your fingers, (the analogy to the three top buds) would become longer.