Your rival is the reason you got up early. Maybe they deserve a nod, not just a glare.

Somebody being slightly ahead of you does more for your effort than any amount of self-motivation. The alarm is easier to obey when you know they are already up. Resentment is the natural reaction, but it is aimed at the very thing making you better, which is a strange way to treat a free coach.

You do not have to like them. Just separate the competition from the contempt. Next time you are in the same room, give the nod. It costs nothing, it usually surprises them, and it stops the whole thing from quietly eating the part of you that was supposed to be enjoying this.