I think you're missing the meaning of white privilege. It doesn't mean white people start out rich and so are privileged. It also doesn't mean that white people didn't have to work hard to get where they are. It doesn't mean that things are given to white people. It doesn't mean that you didn't earn the things you've gotten. I think too many people that are offended by the notion of white privilege think it means they are somehow undeserving of what they have. They equate the concept with what they consider privileged people to be, in general incredibly wealthy people who inherit money they did not earn. That is not what white privilege is at all.
But let's look at your circumstance in particular.
For starters, your parents where white Europeans. It was much easier for them to legally immigrate to the US than it would be for black or brown immigrants. I'm not knocking their legal immigration. I love people who want to come to America in search of a better life. They're exactly the type of people we want here. But that does not change the fact that it was easier for them to immigrate. That doesn't mean easy. It doesn't mean they didn't work for it. It means it was easier. Like on a scale from 1-10 it was a 7 in difficulty for them where it would be a 10 for an African.
Even as an immigrant it was likely just as easy, or easier, for a white immigrant to get a job as it was for a black person who lived here. That doesn't mean it was easy finding a job. It just means it was easier. Racism is still a problem in this country.
When you got your first job at 13, do you think it was more, or less likely, for a 13 year old who was white to find a job than it was for a 13 year old black person? I'm going to guess it was much easier. I got my first part time job when I was 16. I walked in and was immediately hired. I was the only white person applying for jobs that day. I was a fantastic employee but I won't pretend I would have been hired immediately had I been black.
Now let's say there's a hypothetical Kenyan family who wanted to immigrate to the US at the same time. And let's say they had the same intelligence and worked just as hard. For starters immigration numbers would make it harder for them to come to the US. So that puts them, let's say 2 years behind (that's just a guess to illustrate my point). So now they're 2 years behind your family. Then because they're black and not white, it is likely the father would not find work as quickly, and if he did it is likely he would not be paid as much. Now you have a black family who is either poorer than yours or who's mother has to work as well. That robs the two brothers of as strong of an upbringing. Because let's face it, studies show over and over that a parent in the home does a better job of raising children. So now you have a family who is a few years behind yours and whos children are not going to have as strong of an upbringing. Sure, some kids who are in homes where both parents work grow up to be great kids. But a larger percentage of them do not. So now you have kids that might not have the work ethic installed in them to get a part time job at 13. It doesn't mean their parents are better or worse than yours, it means they weren't able to be around as much as yours were and instill the same values. And even if that 13 year old did want a job, he would have been less likely to find one as your were. So now, fast forward to 18 year old you and 18 year old hypothetical kid, which one is going further in life? One is an 18 year old white kid who has a good work ethic and was raised by a parent in the home. The other is an 18 year old black kid who was not raised by a parent in the home. That's a huge amount of difference simply because 1 family was white European and the other was African.
There are reasons that a body stays in motion
At the moment only demons come to mind