What systemic is referring to is that nobody in that situation could possibly rise above it. It is not saying that everybody has the same advantages in life. Some people will absolutely have to work harder, and some people also never identify their true talents which holds them back. Studies show that first born children, on average, do better than second born children, third born, and so on, WITHIN THE SAME FAMILY.I'd argue that this sentence is not only the critical one in your argument, it is also, flagrantly untrue, or at the very least stretched beyond all reasonable bounds of what can be deemed true or false.
If I'm mistaking your argument, that's my error, but my read of this is that you're essentially arguing that there is either, in effect, a level playing field for all people, or that there is at least some kind of equality of potential in all people from birth/youth onward, and that it's simply effort or lack thereof that determines outcomes. That's what I'm referring to as the point that I'd argue is either untrue or beyond any reasonable falsification. It is empirically, factually untrue that there are no systemic issues that hold certain people back. That is true in something as basic as the school system, where the quality of education (and facilities) varies from school to school even just in one city. Someone born and raised in a home situation which has stable parenting, stable and sufficient income, and the ability to access better education and opportunities has advantages over someone who doesn't. People who are, through no fault of their own, born into bad circumstances would have to work enormously harder simply to reach the same level of opportunities as others, and that's assuming that things like race, and income, and anything else that might be brought up don't work against them. It becomes very hard for a great many people to say to people whose situations are terrible that "too bad you were born poor, you should just work way harder than everyone else, and maybe then you'll get ahead of the people with tons more advantage", because that is fundamentally unfair. Does it lead to a lot of fairly-well-intentioned, sometimes-misguided, frequently-poorly-designed-and-implemented policies? Yes. Does it result in some people deciding they shouldn't need to do much of any work on their own at all? Presumably yes. But simply saying that it's all the individual's fault, and implying that there is no systemic issues at play, is at best mistaken and at worst outright denialism in the service of a governmental philosophy often weaponized in favor of the powerful against the weak. (By the way, I do not mean to imply any ill will or malevolence in your argument, just that similar arguments are used dishonestly by some people for political ends.)
You can be born poor, and still become president, or a doctor, lawyer, archeologist... Whatever you want to be, there isn't a systemic (government in particular) barrier that firmly blocks you from getting there. In the past this wasn't always true. If you possess the merits for a line of work but it is impossible for you to achieve it based on the system, that's what I'm referring to. A good example is when MLB only allowed white players until Jackie Robinson finally broke through. Plenty of non-white players were good enough for MLB based on their playing abilities, but weren't given the chance and the system allowed that to happen. That, luckily for everybody, is no longer the case. Back to the doctor scenario, you can be a black doctor, a white doctor, a woman doctor, a short doctor, a hairy doctor, a gay doctor, an any-religion doctor, a trans doctor... As long as you did what you needed to do to meet the standards, including going through the schooling, exams, and residency, you can be a doctor, no matter what other characteristics you identify with.
For fairness, I like to point to something much less loaded than people. Some countries have deep rivers that flow out to oceans and allow them to serve as transport and for port cities to develop. Others have rivers that flow to inland seas which do not facilitate global trading. Others have rivers with giant waterfalls and rapids that make transport all but impossible. Others don't have any large rivers at all.
At the end of the day, a lot of life is the luck of the draw, but in America the original draw does not determine your fate if you don't allow it to. If you drill in to every single person's individual situation, you will find things that are inherently unfair that they have had to deal with. But who is the government to tell us what's fair, and then to take from some in order to prop up others?
Also, at the end of the day, you have the ability to help determine the fate of the next generation by the parenting you provide to your children. My parents worked hard to put a roof over my head. Why should they be asked to support anybody else's children other than their own, and why should anybody be expected to support me if not my parents themselves? We all have to be individually responsible for ourselves and stop expecting the government to come save us by incrementally putting our freedoms back into their hands. So no, life isn't fair, but the opportunity is there for everybody who chooses to seize it and has the fortitude to live out their dreams.