What if McDonald's was in charge of the entire education system. Do you think they would teach in a way biased towards McDonald's or Burger King? There's no difference with government. The very act of arguing against this question shows that the government has taught you to trust them. Public education will inevitably teach that we need the government. Also, the lack of competition gives us the expensive and terrible quality schools we have today. Hitler had a Nazi Youth program, do you think that's a form of indoctrination?
Public schools are like any other school they encourage us to further our own education and believe how we want. They teach the students freedom of expression and to think in new and amazing ways we may not have thought of. Public schools are just as good as any other school.
Public schools do not indoctrinate. They educate, and they form an essential purpose in promoting literacy and gaining the skills one needs to become a responsible citizen. These schools need more funding. The current craze for charter and private religious schools are doing a lot of kids a profound disservice.