The Pfizer trial had about 20,000 people in each arm. That's just not enough data to detect rare side effects at a rate anywhere near high enough to know that the vaccine is safer than covid itself for younger/healthier populations who aren't at risk. For the young, healthy, 0 to 19 age range the infection fatality rate of COVID-19 is around 1 in 2.5 million: https://gh.bmj.com/content/5/9/e003094

Normally that wouldn't be a big problem, as vaccines are usually rolled out relatively slowly, so population wide monitoring should pick up on any issues. But countries are aiming to vaccinate as close to 100% as they can get within a matter of months.