Perhaps the major thing Family Guy tends to exaggerate is family life. It takes the traditional family of a husband, a wife, kids, and a pet, and presents them with exaggerated magnitudes. When you look at Peter, the father and husband, he represents the everyday family man. He is the one that works, and always has the support of his wife in tough situations. But, no man like Peter Griffin exists. No one that is psychologically healthy behaves and makes the decisions Peter does that require such support from his spouse. One example of this is when the mafia placed a hit on Lois. Peter and Lois were then invited to the wedding of the Don's daughter. When granted one favor by the Don, instead of asking him to call off the hit as Lois advised him, Peter instead asked for a pie that the Don was eating.
Meg & Chris
When it comes to the kids, Chris and Meg, all aspects of being a teenager are exaggerated to show the public the general view of being a high school student. Meg's low self-esteem and concern about not "fitting in" are expressed in the most dramatic ways. She is always crying and always lies about having friends. An instance of this is when Meg tells her parents that she is going to the mall with her friends on Saturday. She is then shown at the mall's food court spying on a bunch of high school kids eating. When the kids depart, Meg runs to the table they were eating at, and starts eating their leftovers. Also, Peter is always making fun of Meg. He puts boogers on her and calls her derrogatory names. This might be a way of exaggerating the lack of support parents give their teens. When looking at Chris, he is used to exaggerate the teenage male. He does the stupidest things. He is a pervert, a drug user, and also struggles in the social world when trying to fit in and having crushes on girls that don't like him back. In one of the episodes he strives to impress a girl who is manipulative. This girl wanted to ban gay marriage and bribed Chris into letting him touch her boob if he destroyed Brian's petition. In the end Chris burnt Brian's petition, but didn't get what he wanted.
When looking at the family dog, Brian, one can see that a dog being a "man's best friend" is slightly exaggerated. Aside from the fact that Brian is given human qualities, he is best friends with Peter. Peter has such a great bond with Brian that sometimes he tends to listen to him over his wife. For example when James Woods stole Peter's identity, Brian conveyed to Peter that the only way to get back at him was to steal Woods's identity. Lois completely opposed this saying it would only cause more problems. Peter ignored Lois and listened to Brian, and surely enough it led to more problems. ("Back to the Woods")The "Beauty and the Beast" article further helps convey these points as the author talks about how other sitcoms such as The Simpsons, have taken the approach of keeping the norm of a traditional family in tact while providing a different cultural view. As the author explains the "norm" of what is customary in our society, is constantly changing or grasping new ideas, and subliminaly, this is the way shows like Family Guy show it.