Why do trees grow downward in computer science?
I have a feeling it goes back to a printer, and that a program traversing a tree first prints the root, and uses the notion of a bottomless stack of paper to express the indefinite levels of recursion that might be encountered.
Trees grow downward, having their roots at the top of the page and their leaves down below
by convention, trees are drawn growing downwards
From the Wikipedia article on tree data structures.
Real trees grow from their root upwards to the sky, but computer-science trees grow from the root downwards
From David Schmidt's lecture notes.