Why do many people think homeschool isn't an actual education?
Because you're at home. I don't believe that but that's what I've been told.
Because few pupils actually do their homework as it is, so why do it ALL at home?
Often because of the rationale behind homeschooling. My daughter is homeschooled and does very well with the public curriculum. However, lots of kids are homeschooled to be “protected” from things like evolution, sex education, etc and instead brainwashed with religious dogma and a medieval scientific understanding.
Because a lot of people see that you are not going out and being taught by actual teachers and they automatically think that your not getting sufficient education.