I have been the bullied, and the bully, in US elementary schools during the 90s. Never on a consistent basis, like you hear about in US popular culture.
All my memories since 3 years old are of feeling like an outsider. Strong cliques were present even in kindergarten. I suppose this is because my elementary school was in a dense neighborhood, so kids from there were more likely to share social bonds both in and out of school. The further away your home was, the more socially disconnected you were, and the outsider feeling was probably a consequence of that.
It was always after school, when hordes of kids went mostly unsupervised on the campus, when the bullying happened. I was usually alone. I liked to draw pictures. The bullies called me names, stole my papers and pencils, and hit me when I wouldn't give them away.
I had friends at school, but most of them were picked up by their parents soon after school ended. I had to wait on campus in "after school" for hours until one of my parents drove from work to pick me up. Maybe it was my fault for not wanting to join in with the other kids. Maybe it was because my parents told me all the time that I was special that I thought I was better than everyone else, and couldn't waste effort on being with them.
Eventually, I figured out that bullies leave you alone when you hit them really, really hard. In halls where no teachers watched, there were fights. By the end of Elementary School, the kids who all bullied me were shorter than me. I began to play rough. I confronted one member of the in-cliques in the middle of the cafeteria, knocked the wind out of him, and just walked away. No one stopped me, and no adults were present to intervene. I wanted people to believe that I was dangerous, and succeeded at that.
Some time after that, during after school, there was a kid who seemed smart and interesting to me. Learning about him, he mentioned that it was dangerous to hit him on the head, because he was "epileptic." I had never heard of this "epileptic" thing before. I wondered, what would happen if he was hit on the head? So I hit him. He exclaimed something like "Noooooo! Don't hit my head! Don't do it!" To which I thought, "Hah. You had better try to stop me then." So I hit him again, and again, and again. He didn't do anything to stop me physically, so I kept doing it. After a dozen times, it started to bore me, so I finally left him alone. Later that afternoon, I felt guilty about what I'd done. I don't remember if I apologized to him or not, but I hope I did, because I'm pretty sure this counts as bullying.
It's an incredibly intoxicating feeling to put your own amusement above the needs of others, especially when you can justify it. ("Oh, I was just trying to learn about epilepsy, and he's also weird.") Exploiting the perceived weakness of others to be in control of the situation makes you feel powerful, even more so when you've already experienced the same thing the other way around.
Becoming comfortable as a dangerous outsider gave me a reputation of being an annoying ass who nobody wanted to be around. Socially, I was stunted, and it's taken a lifetime of personal development to break through some of that.
To address your question "Is it because of the Croatian nondemocratic socialist government heritage? Or is it an European thing?" I cannot speak to Croatia, but I did go to the Netherlands for a few summers as a kid. It seemed like the kids on the playgrounds there were consistently mean to me too, and sometimes I would act threateningly to show them that I wasn't to be trifled with.