Education in it's current form is not a way to fight poverty. Churning out people who can pass a standardized test and attempting to fit them to a mold solves no problems. If education is to truly attempt to fight poverty then it should focus on learning, and providing apprenticeships for people who do not want to focus on STEM learning. A more individualized approach should be taken, which obviously can't be done without an increased budget. To say that the only way to fight poverty is through education is a farce though.
While we don't have the vocational structure that other countries have, we have a pretty decent one. I have a couple of friends who decided to become aircraft mechanics after highschool and they are doing pretty well. They attended a 2ish year program and almost all of them had jobs right after graduating. I think the issue is that people often look down on these programs and think that they aren't as good as going to college, which sucks because my friends are making really good money and they really enjoy working in that industry.
Who can be against improving education? That's why its a perfect thing for politicians to focus on. Not only can you appease the wealthy, but you can tell the poor that you are working hard on improving their lot. It's a similar thing with cutting science funding and saying we need more science education.