Note: This is in no way a professional opinion, just what a girl who has lived in New Zealand for most of her life thinks.
Firstly, I'd like to clarify the word 'hate'. By hate I don't mean that girl you dislike because she's always picking her nose, or the person everyone publicly dislikes, but I mean that person you glare at across the room. Maybe they're your strongest competitor in a class, or your ex best friend. They're usually the person you want to beat in everything, the one you don't want to lose to no matter what.
Does someone come to mind when I say these things? I'd say it's likely you're thinking of someone right now, whether you used to know them or still do. Maybe this rivalry was ancient, but that doesn't matter. Why do I think you'll eventually like them? Just think. In order to "hate" them, you need to know a lot about them. With these people, you don't hate them because everyone does. In fact, people probably think you guys are crazy in your hating each other, and you always find yourself explaining your logic.
The only way you can become enemies with someone is when you get to know them and have a long list of things you dislike about them. Personality is a big factor in this. Perhaps, you don't like that girl because when you look at her, she reminds you of all your insecurities with her personality which is so close to your hidden one.
So there you have it, why I think you'll eventually grow to like your enemies. Whether this is romantic interest or not, I reckon your rivalry could easily grow into a strong friendship.