the purpose of PE, as it currently exists in the American school system, is to prepare kids to join the military. that's not some sort of moral-panic hyperbole. that's...pretty explicitly the purpose.
most of the prominently nightmarish features of PE, such as running the mile or doing sit-ups, originate with the Presidential Fitness Test. This test, which president Eisenhower implemented in schools in 1956, was created after a different fitness test (the Kraus-Weber test) revealed that Americans were less fit than Europeans -- specifically the Swiss.
The difference between the Kraus-Weber test and the Presidential Fitness test is that the Presidential Fitness test was specifically designed to test military fitness. While the Kraus-Weber test measured total fitness by testing things like core strength and flexibility, the Presidential Fitness test doesn't really make much sense in the context of ordinary fitness -- only in the context of military fitness. Do you remember being tested on how far you could throw a softball? That test mimicked throwing grenades. And it's pretty easy to see why Eisenhower went this direction. In 1956, the Cold War was in full swing and WWII was barely in the rear-view mirror. There was a real possibility that we would be at war with parts of super-fit Europe in the near future. Eisenhower wanted the nation's children ready to fight in that war.
The main issue with the Presidential Fitness test is that, as pointed out above, it really doesn't teach kids how to stay fit or incorporate physical activity in their day-to-day lives. A soldier at war might need to run a mile with no warm-up, or perform a pull-up, but for the average middle-schooler? The tests were just kind of...pointless exercises in misery. You're only really good at the Presidential Fitness Test if you've been practicing the specific exercises tested. And what 12 year old child is doing pull-ups for fun and pleasure? So instead of inspiring America's children to train themselves into a super-fit army, it just humiliated kids who didn't perform well.
There's been a recent push for PE classes to focus more on life-long fitness (things like actually teaching kids to warm up, exposing them to different types of physical activity, etc). Unfortunately, the Presidential Fitness test has already done its damage. It continued to be used in schools until 2013. That's 60 years of teaching kids to associate physical activity with shame and dread. The idea of military PE classes is pretty much baked into our cultural memory, giving us all a background dread of physical activity. and guess what, eisinhower?? that's just going to make people less likely to be physically active!! Maybe if we're trying to emulate the fitness of the SWISS, we shouldn't have gone with MILITARY TRAINING FOR CHILDREN!!
anyways. take some comfort in the fact that nobody will ever judge you for your mile time again. and if they try, ask to see them run a mile. directly away from you.