Why does Family Guy have cursing?

Answer 1

No one can really answer WHY. It's simply the choice of the script writer to have the characters curse. Or perhaps it's the choice of the voice artist to have them do it because the line is funnier with a curse than without.

Answer 2

Because most jokes, situations, language, and other types of comedy are suited for 14 year olds and over. In addition, there are scenes of nudity(partial nudity) that most people under the age of 14 cannot handle until they're old enough to understand.