I personally always considered an enemy as someone you hate. Hate is not something I have for too many people, if any. Just people I strongly dislike, so based on that I don't think I have any enemies. That being said, I would think of an enemy as one who wanted to destroy me rather than me want to destroy them. The main reason being I don't have hate for anyone, so I don't wish to destroy anyone. I suppose rival would almost be the same thing, but my best friend is my rival in many things but I don't think of him as an enemy per say. I do think you can learn from your enemies, but I would learn in the form of understanding them; the way they think and process the world around them. I would then think about how I could apply that mindset to my life if applicable in a way that would better me as a person.
