Okay, a lot of people are missing entirely the point of what I said. I'm not asking about someone who you compete with to get better, I'm just saying someone who you train with that constantly drives you to train harder, someone that keeps you focused. Bear in mind that there are some places where your fellow students may not work as hard as you, and so you're forced to take it easier than you would like to.
I think I understand you and can come from a similar situation.
all my friends are martial artists to some degree as are my brothers. When one of us goes up a level in skill the rest of us seek to find a way to match it most of my friends are decent training partners, but I would consider two of them to be rivals in a sense.
I think it is important to train with people of all different sizes and shapes to better round out ones ability, but I think most people have a few favoirte training partners.
My brother was my first rival. He's 3 years younger than I and is a MMA as well as a 3rd dan in Isshin ryu karate. He and I would go back and forth comparing techniques under different kinds of situations. We used to spar a lot (MMA style) which he was far better at than I was, so he would get the best of me there. I would take my losses and turn them to lessons to find ways not just to beat his technique, but to beat people who could possibly fight like him. In turn I would help him improve his practical self defense skills. There were times when I would get upset thinking I wasn't good enough at a certain thing (cause he'd be better), but then I realized that his method was not the route I wanted to go and so after I realized that I was able to imporve myself a lot more.
My other "rival" is my favorite training partner at my dojo. His name's mike and he's a good 60-70 pounds smaller than I am, but in far better physical condition. We've trained so much together that we know exactly how we will react to each other when a certain type of attack is given which allows us to experiement more and try to change it up and turn up the heat a bit more than we can do with other training partners. Mike has been a good way to measure my skill, as we improve at roughly the same speed and test for ranking together I can compare how well I am doing by watching how well he is doing. We try to out do each other during training, to see how we will react to each other, but it never became about beating each other at anything, it became about how can we improve faster?
My teacher noticed how much tougher mike and I are with each other, and has sort of forbidden us to train with each other when other black belts or higher ranked kyus are available. He doesn't want us to be so used to each other's body type that we react poorly to different people. But we still attack each other and test each other in a friendly way. I like training with the other black belts and higher ranked kyus as well ( I get to try different things with them), but mike is my "rival" I guess because I know the ins and outs of his technique and he knows mine.