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Sometimes to answer a question the gemara will start out by saying "ileima...". The structure of such an answer is as follows:
"If you want to answer this way, you can't for such and such a reason, rather the answer must be this".
If the initially suggested answer is known to be incorrect, why even suggest it in the first place?
The proof essentially functions as a process of elimination: by showing that the alternate explanation is not viable, you demonstrate the validity of the acceptable explanation. Also, if the gemara only gave the correct answer, the reader would never learn how to analyze and reason on his own. "Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime."
