As zenvelo points out, it’s largely because the show contains a significant amount of sexual, disgust, and violence humor. Some parents also dislike the show entirely and think that it is simply not funny.
Personally, I think Family Guy is all right – it makes me roll my eyes a lot, and it’s so over-troped it can get pretty boring for stretches, even though the over-troping itself is a way of poking fun at other sitcoms. I get it, it’s just not funny. However, I also get a laugh surprised out of me about twice every show. Some things are very well done, like Brian acting like a real dog. “Hey Lois, there’s another dog in that car! Hey! Hey, other dog! Fuck you!” And comedy aside, the show sometimes makes frank and insightful comments about modern life – can’t think of one off the top of my head, but they’re in there.
And, zenvelo, it’s not as though the kids’ shows are really all that much less violent or disgusting (I’ll give you the sexual humor, mostly) – take Ren & Stimpy or Invader Zim, for example. Hell, if we want to go more recent, I flipped past a Saturday morning cartoon the other day that centered around three sumo wrestlers using their really graphically drawn enormous butts to fight evil.
Finally, potty humor has been around for a really long time, and some people love it. It may not be your cup of tea (it is not mine), but it’s unfair to characterize such jokes as across-the-board “not funny”.