It’s surprisingly easy to teach racism and sexism. Parents do it all the time very effectively. Not long after MLK was killed there was a classroom experiment done, which was later made into a documentary called Blue Eyes Brown Eyes. The whole documentary is an hour long, but I think even watching a shorter 5 minute clip from it will show you just how quickly kids pick up on bad behavior when authority figures feed it to them.

And there are so many other good answers that other people have already written. It’s really neat to learn from so many perspectives.