What social statements are made in the movie October Sky?

The big social statement lurking beneath the feel-good story of a small-town kid who got out is that small towns are dead ends. Never mind the solid coal-mining families of the West Virginia mountains. Never mind the loving father who just wants what he thinks is best for his kids. October Sky wants you to think small towns are dying and that on their way out, they'll kill you if you don't escape. That may be true, but it didn't have to be true.
In the movie, small towns and coal mines are stifling, retrograde communities, where the only hope of a decent life lies outside. Reach for the stars, the movie is literally saying: no fancy cars or pretty girls for you here. No education, no future is possible here except what you already know. The town and its mining families aren't explicitly denigrated, but the message is inescapable.
The thing is, history has proved that right. Small-town people often grow up and leave, then look back on their lives as if their upbringing was a problem or the cause of other problems, even as they lament the loss of the good things their childhood gave them. A great example of that is J. D. Vance's book, Hillbilly Elegy. It's fantastic, and I highly recommend it if you'd like to further explore some of the social issues touched on in October Sky.
https://eppc.org/publications/october-sky/

https://www.nytimes.com/2016/08/11/books/review-in-hillbilly-elegy-a-compassionate-analysis-of-the-poor-who-love-trump.html

https://www.wpr.org/rocket-boys-memoir-aka-october-sky-homer-hickam-jr