“Biological superiority” is the belief that a race is inherently superior to another because it is more evolved, usually claimed around intelligence. This is a well-understood term. Just Google it.
“Classical Racism” is clear from the context. I’m not referring to the new definitions. But, I didn’t coin the term. You can Google it too. Here is a book from the Harvard library that uses the term in the title. https://dash.harvard.edu/handle/1/4833818. If you read much on race, the term can mean systemic racism, institutional racism, etc. I am using the dictionary definition listed first if it has more than one.
So, now that your attempt to start by discrediting me intellectually has backfired, let’s move on to answer your questions.
“…there’s nothing necessarily wrong with believing yourself the best. What matters is how they actually behave, not what they think and believe.”
If an individual wants to think of himself the best and has the grounds to do so, there is nothing terribly wrong with that — other than it may make him rather unlikeable. Even a lot of Trump supporters find this aspect of his personality rather annoying.
There is something fundamentally wrong with believing your race is superior because it isn’t true. It’s delusional. Differences in traits between races on average are minuscule compared to the individual differences between members within races. If one believes he is superior by being a member of a certain race, then they are factually wrong.
Note that I did not say culture. One culture can be superior to another empirically, depending on the characteristic you chose to measure. My point is that often culture and race are aligned. For example, in the case of white colonialism, the culture was superior at shipbuilding and weapons-making. This led the white colonialists to believe that this meant they were superior as a race. They believed they had a biological, evolutionary advantage that was a justification for their behavior, which included justification of enslavement.
Now, if you are saying there is nothing wrong with believing your race is superior as long as you keep it to yourself and don’t act on it, then other than being a fool, there is nothing wrong with it. The problem is people never keep it to themselves. They do act on it. In the cases of all the groups you mentioned, there are atrocities that go along with their belief in superiority. Even if they don’t individually act on it, the system they are born into because of it created unjust privileges.
As for American pride, there is nothing wrong with being proud of achievements. It’s how you behave, as you say. I hope that when China is as powerful as the US it isn’t as heavy-handed in its sense of cultural superiority, but I doubt that will be the case. It always seems that those that think they are great believe this gives them license over the less great.