I think it always help with AppleScript to keep in mind “who” (i.e., what) you are addressing with your commands.
When you write ‘tell application “Finder” ’ remember that the verb “tell” is not being addressed to the Finder. It’s being addressed to the parent script object in which that tell block resides. It has the form “the parent script object should tell the application “Finder” to…"
The commands inside the tell block, however, are being addressed to the Finder directly. So the command
convert_the_file(the_file)
is equivalent to
tell application “Finder to tell its handler convert_the_file(the_file)
Finder responds with an error because it has no such function/handler. Inserting the ‘my’ redirects the command up to the parent script object, which of course does know about the function as that’s where you’ve declared it. i.e.,
tell application “Finder to tell my handler convert_the_file(the_file)"