[D]ropping out...[is] quitting on your country, and it's not an option -- not anymore.
Granted that political speeches often contain exercises in hyperbole, in this case President Obama went too far. He is saying that dropping-out is akin to treason.
America is free country -- and part of freedom is freedom to do unwise things. It is truly unwise (for the vast majority of people) to drop out of school. But they should be free to do it.
We should counsel young people against dropping-out; we should have research-based programs that discourage it and that try to get people to come back to school. (The Doing What Works website is scheduled to post research-based material on dropout prevention later this year.) But we should not end dropping-out by blocking the possibility.