Conjecture, but it may be to focus on the native born population as a better metric for education quality since they have (presumably) been a product of that system for their entire life. Contrast that to a 1st gen immigrant who a major amount of time in a different country's system; testing them after a short stint in the US tells us much less about the US educational system. It's harder for me to think of a reason why 2nd gen should be removed, unless the assumption is the educational attainment/integration of 1st gen parents heavily biases the results of their kids. I don't know if all that holds up under scrutiny, though.
Also, because demographics aren't distributed evenly geographically, I think there is probably a case that the education system is different for different races (to the extent that racial geographic distribution is different).
2nd gen are removed so that there are fewer poor people with uneducated parents who can't help them at home because the school system is bad in the sample.
That's what I was alluding to, but it's unclear how sound of a methodology that is. It seems like a better approach would be to control for parent educational attainment directly, rather than use some imperfectly correlated metric like immigration status.
Also, because demographics aren't distributed evenly geographically, I think there is probably a case that the education system is different for different races (to the extent that racial geographic distribution is different).