People who don't achieve a whole lot do NOT think they are great or superior people. People who DO achieve a lot DO think they are BETTER THAN OTHER PEOPLE. I measure arrogance by how they view themselves in comparison to other people.
Then that's not the definition of arrogance.
If someone is good at something, they're qualified and correct to say that they're better than the other person at that thing in some contexts, or to simply be proud of their achievement. It's not arrogance, it's true.
What makes it arrogant is when other people are put down for their lack of achievement, or when the assumption is made that one is also better at XYZ unrelated activity as a result of success in another. e.g. "I have a PhD in physics, so I know how ecology works!" or, "my IQ is higher than yours, so I know better!" or, "I'm an INTP -
the most logical type, so what I'm saying is logical!"
The key point is that this is an exaggerated sense of self-importance, relative to one's actual achievement or ability.
To accurately sum up your own abilities as effective and to consider yourself talented at a task, isn't arrogance if you actually are good at something.
I agree, people who achieve a lot, who think they're better than other people as a whole, are probably arrogant. People who achieve a lot, who think they're better than other people in the areas they've achieved and excelled in, are justified in their belief.
The thing that makes something arrogant, is when someone's sense of ability or importance is
exaggerated. Not all pride in one's work or confidence in ability is arrogance. It's healthy and positive to be happy with your achievements and abilities.