It's the biological inaccuracies for me.
Your body has a defence mechanism I'm sure we all know as immunity. The idea is you get sick, and then you don't get sick again.
To get more into detail, your body has cells called B-lymphocytes. These lymphocytes are each unique, all different and all ready to deal with a different kind of pathogen, even if it's unknown.
When you get a disease for the first time, your body doesn't actually know which B cell can deal with that pathogen. So it spends some time trying to work out which B cell can deal with the virus, and then once it is found, the cell multiplies as it produces the antibodies to deal with the infection.
This process takes up to 15 days. During that time you will fall ill, and then recover towards the end.
Now your body has Memory B-lymphocytes. These will remember the virus and act much quicker and more efficiently - 3 times faster and producing 100 times more antibodies.
What vaccination does is it gives you a dead form of the virus. It's just the viral shell, really, but your body doesn't know that and reacts to it in the same way. It ensures that your response to the virus will be quicker and more efficient than if you were unvaccinated.
But it doesn't make things perfect. A lot of people think vaccine should equal you never get sick, but that's just not the case. Even in an immune person with memory cells it still takes the body several days to have enough lymphocytes and antibodies to properly deal with the infection. Often the virus doesn't incubate in that time or present any symptoms but it still does, and it still can.
If you're vaccinated and you fall ill with what is confirmed to be coronavirus, it means you've gotten a pretty aggressive bugger. Which is not unrealistic, and not taking into account that viruses like to mutate which can present difficulties. But if you weren't vaccinated and got that same sickness, your response is going to be 3 times slower and much, much less efficient.
The vaccine by and large turns hospitalisations into a "sit home and rest" situation. It turns sitting home and resting situations into being asymptomatic and just waiting for your body to flush it out.
Just because people are getting sick with the vaccine doesn't mean it isn't working. It just means they would've gotten more sick had they not been vaccinated.
Rant over.