In the same mindset, what good is a country with no ruler? "Divided, leaderless." Also, it was possible for the battle to be won (thus Mordor defeated, Rohan safe) but the leaders of Rohan to die still. The leaders' deaths (or even the death of all of the Riders of Rohan) do not guarantee a lost battle and Rohan's destruction - that is a logical fallacy.
It was the obvious choice to make. Eomer or Eowyn... Eomer has been trained all his life, a great soldier. It's not immediately because she was female that he was chosen over her, it was because she was weaker and less-suited for battle (whether this is a consequence of her gender or not). Additionally, her responsibility as a citizen of Rohan is not only to the people of Rohan, but to her king. Whether it turned out for better or worse, she disobeyed him.
__________________
...take counsel with thyself, and remember who and what thou art.
|