I have 4 kids, so let me give you a view into my life:
My oldest has always, always, been super independent. On her first day of preschool, she walked away from me without tears, a hug, or even a backward glance. I felt pretty useless! But as others have pointed out to me, she uses me as her touchstone--she knows I'm there, so she can venture out. She has always followed her own path, totally fearless. Even though she was the smallest girl in her grade, the bus bully was afraid of her--he was twice her size. She chose her own path through HS, getting crap from friends for not having a "better" goal and taking more rigorous classes. She graduated 20-something in a class of 400 and got into her dream school--a large, thriving urban campus. Double-majored (elementary/bilingual education), did a semester abroad, and is now teaching English language learners, 800 miles away. Sigh!
Kid #2 was totally different. Major health and developmental issues in his first five years. Many, many rounds of testing to figure him out. We finally got answers a couple years ago--he's super smart, but has Asperger's, anxiety, depression, and 2 learning disabilities. He's also off-the-scale introverted. His path is murkier, but he's attending community college while living at home, and he's on meds. I don't see him living far from family, although with help, he can probably find his niche.
Kid #3 was very anxious as a child, but has grown to be uber-social. She, too, takes no crap from anyone, and is super friendly. Ironically, I think moving in 7th grade helped her to empathize with new kids, and give her the skills to make friends easily. She's hoping to be a prosecutor, so she can be the voice of the victim. In HS, she doesn't hang out with the "cool kids"--she's very loyal to her group of friends from middle school. For now. That may change as years go on--DD is in the IB program, which is quite rigorous, and only one of her friends also chose that route.
Kid #4 (my baby!) is very laid-back, but he also doesn't care what people think of him. He has friends, but not a whole lot of them. He loves color and dance, Boy Scouts, and the violin. He'll wear a tie-dye shirt every day of the week, and doesn't care what anyone thinks.
I think, when you only have one kid, it's easy to look to yourself as to why they do certain things, or are a certain way. Don't flatter yourself!
I wish I could take credit for my oldest being so independent and focused and confident. She literally was that way when she was a baby! I marvel at it, mostly because I don't know where it came from. I do think it's important to think of how a child's specific personality traits can get them into trouble, and maybe work to smooth out the edges, i.e., speaking your mind is fine, but maybe not to the principal if you think he's wrong during an assembly.