>And it is possible for a poor person to encourage their children to study and become a doctor or engineer (see for example the Asian immigrant communities).

The Asian immigrant communities benefit from a much more stable environment than other immigrant or domestic communities have (and less systemic racism and exclusion). The same is not the case for the black or latino communities for example.

And even if the child of poor immigrant community (Asian or whatever) studies hard to become a doctor or engineer, they'd still have to do it under less opportunities, with less connections, more sacrifices, in worse school districts, with less access to tutors, with more stressful family environment (even less nutricion, more need to move, in more dangerous neighborhoods), etc than the child from a upper middle class or rich family. That's the injustice and lack of meritocracy.