Why exactly can't Microsoft Word close if there's a dialogue box open?

Because most dialog boxes are considered "modal" which means that control does not pass back to the main program, or calling container, until the dialog itself is closed. This is by design and the programmer has the option to make a window modal or non-modal. Usually, a window is defined to be modal if the main program cannot or should not continue until the opened dialog is dealt-with either through selection (Ok) or aborting (Cancel).

The dialog box might be saying something like:

You have made changes to your document, do you want to save them? (Yes) (No)

There is no obvious right answer here. You may have accidentally corrupted your document (for example, the cat walked over the keyboard) in which case the answer is "No", or you might have spent hours typing in changes in which case the answer is "Yes".

The safest thing for Word to do is is refuse to close until you answer the question.