Problem: How and why does Beethoven imitate a funeral march in the second movement of his 'Eroica' symphony?
In order to answer the question 'why' you will need to relate the funeral march of Beethoven's Symphony to the context in which it was written.
The political and philosophical environment of the early nineteenth century provides the broad context in which Beethoven worked, especially the events of the French Revolution and Napoleonic wars, and the idea of the Hero. You will need to consider how these elements are reflected in the Symphony.
The music of other composers would undoubtedly have had an effect on the type of music written by Beethoven. You will need to consider how this broader musical context affected Beethoven's composition of his Third Symphony.
You will also need to consider how Beethoven's own political sympathies and philosophical beliefs shaped the approach that he took to writing the Eroica Symphony.