Respect the rival who pushed you. Without them you’d still be at your old best.

Someone who beats you regularly does something for you that encouragement cannot. They set the height of the bar and keep it there, and they make the parts of your effort that were only performance impossible to sustain. Feeling grateful about that while it is happening is nearly impossible, which is fine, since the gratitude is usually retrospective.

Say something honest to the person you are chasing, even just that they are good. Then take one thing they do better and work at that specifically. Rivalry is far more useful when you are studying them instead of resenting them.