Why is literature a difficult term to define?

While works we would now consider literature have existed for several thousand years, dating back before the invention of writing, literature being used as a category is relatively recent.
The ancient Greeks had several terms referring to what we now would call literature. Poetry, divided into drama, epic, and lyric sub-genres, was understood as a genre. Prose fiction was not developed until late antiquity. In general, poetry was considered part of the educational discipline of grammar, and taught as part of instruction in reading. Prose, and the art of prose composition, fell under rhetoric. In Latin, similarly, poetry was part of secondary education in "letters." The study of style was equally applied to prose and poetry, and included examples from the poets, Plato, oratory, and history.
Our modern notion of "literature" as something distinct from pedagogical environment and meter (or lack thereof) is essentially Romantic and tries to divide literature from nonliterary texts using somewhat vague criteria of creativity, quality, or style. Such criteria, are, unfortunately, subjective, making defining literature in the modern sense rather problematic.