Why are old cartoons so racist? It shows Black people with big lips and showing watermelons? Why?

How is that racist?

Because those were stereotypes that were used to more or less make black people seem less human than their non-black counterparts, whether or not that specifically was the expressed intention of those who were using it in the cartoons.

@GoldenXena: How can they be racist if they didn't intend to do that?

Because being a racist is not intention dependent. You don't need to wring your hands with 'I am going to do X nefarious thing with the expressed goal of harassing you or dehumanizing you based on your race' going through your head. In fact a lot of the bias that leads to that is generally taken for granted by the people with them. I think Avenue Q said it best, everyone's a little bit racist sometimes, the creators of those cartoons were just more than most we have today.

@GoldenXena: Makes sense. Thanks for your input :)