Satire is when taking an existing concept and drawing it to such absurd extremes that it becomes funny. Example:
American Dad is a show about Stan Smith, a conservative CIA agent. Stan lives with his pretty wife Francine, that’s so stupid that if Stan points into a wall and says: “we need to run that way,” she will run into the wall and say: “it’s a dead end!” Stan is so conservative that when Francine says that she likes being spanked, he drives her into the woods until she has “purged her sick desires.” Stan also lives with an alien he holds refuge from the CIA and a fish that has the mind of a German athlete because his agency has a mind switching machine and kidnapped said athlete to switch his mind with a gold fish to keep Germany from winning the Winter Olympics in the 80′s.
American Dad is taking the existing concept of right-wing conservatism and drawing it to absurdity.
American Dad is satire.
Family Guy is a show about Peter Griffin, a sexist, racist alcoholic who neglects his family. He is married to Lois, who starts off trying to care for the family, but eventually sides with their abuser and, to a lesser extent, picks up drinking and eating disorders herself. Peter bullies his teenage daughter Meg, and gets the rest of the family in on it, to the extent that Meg self-harms, binge eats, and completely internalizes the abuse.
Family Guy is taking an existing concept of familial abuse and draws it to an extent that is not absurd or even rare.
Family Guy is not satire, it is bullshit that thinks it can use satire as an excuse to be harmful.