Have same feeling when i am commuting or jogging.

If there is another cyclist or runner in front some instinct gets activated. I follow it partly, just getting a bit closer (still plenty of distance inbetween) and maintain the same pace. Once i see that i can do it easily i stop "the race" and get back to enjoying the ride. If the rider in front notices me and starts racing, well, then let the race begin. Does not happen too often.

If i am getting passed and see there is no way to keep up then i cool down and somehow feel sympathy for that person in front.