In first place, racism and sexism are a kind of social exclusion, because you feel yourself superior than other persons just because they have another skin color or another gender, and you enjoy letting them to know that you are "better". For example, I've heard people telling they don't want to travel by bus/ taxy/ subway/ etc, next to black skin people, because they "shouldn’t be with white people". Considering that average chilean people is not blond hair with blue eyes, that's a stupid reasoning.
In addition, sexism and racism are horribles kind of violence: you feel yourself with the right to mistreat /to force /to bully someone just because that person has a different skin color than yours. For example, since three weeks ago, a Monday in the morning, I was walking on my way to take the subway, and in front of me came walking a beautiful afro-descendant girl, who was fully dressed with school uniform. There was a building in this street and men working on. when they saw her, they started to shouting at her a lot of xenophobic and sexist phrases, allowing to her body, her hair, her skin color, etc. The girl became intimidated: she started to walk very fast and she covered her ears. She wanted to disappear.
Finally, racism and sexism are weapons that politics use to deal with each others. I mean, together we are stronger, but separated we are weak, and that is what they want to: make us weak to keep enslaving us and continue plundering Latin America, Africa and Asia Minor.