Given the scale of both normal disease occurrence and of the vaccination campaign, it is expected and normal for a very large number of people to get sick after vaccination - simply due to chance.
If you read into that purely statistical statement a claim of vaccinations not having any side effects than you need to read what I wrote, not what you think I wrote. One has nothing to do with the other, and I'm only addressing the one thing. Of course you can have problems due to vaccination, but you can not "hand-wave" any single random event into that category, especially when it's obvious you fail to even consider the large amount of "normally sick" cases that are bound to happen simply by random chance of them occurring all the time either way.