Because breaking out of poverty is a hard thing to do. It is certainly possible, beginning with a focus on achieving at a high level early in school (which can be a difficult task when dealing with life issues imposed by poverty). Doing extremely well in high school, which can lead to college, scholarships, etc. is one of the few exits on the freeway to adult poverty for impoverished children. Once that ship has sailed, they could go into trades, such as electrical and plumbing/heating. Most, won't, instead bouncing from job to job with no hope of ever improving their station in life, and will have their own children, instantly worsening their own financial situation and continuing the cycle.

But none of that means it's impossible or that it requires luck to break out of (again, assuming they live in a country with abundant economic opportunity). It requires hard work, discipline, and perhaps most importantly, an understanding that the limits their parents ran into that resulted in their impoverished upbringing are not insurmountable.