Also, more old people are vaccinated, but even with a vaccine, older people are still more vulnerable to covid.
Imagine you have 100 people over age 80 of whom 90 are vaccinated, plus 100 people age 20 of whom 20 are vaccinated. Now you have 20 people in hospital - 17 of them are old (12 vax-ed) and 3 are young (all unvaxed). That means that 15/20 people in hospital are vaxed, which you might think is bad.
BUT - look just at the old people - 90% out of hospital are vaxed, only 70% in hospital are vaxed ==> the vaccine helps. And look just at the young people. 20% out of hospital are vaxed but 0% in hospital are vaxed ==> the vaccine helps.
This is a statistical error called Simpson's paradox. If you look at the whole population, you can end up with the wrong conclusion because different groups (old / young) have very different starting points.
There is a more detailed explanation here
www.ntu.ac.uk/about-us/news/news-articles/2021/11/in-the-wrong-hands,-vaccination-statistics-can-prove-deadly-simpsons-paradox-shows-why