The details
Intuitively this does seem like the best option: leave the family home, produce your own offspring, thus ensuring that your genes make it to the next generation. If you think about it, though, by helping your parents raise their subsequent broods (i.e. your brothers and sisters) you are getting some of your genes into the next generation. You have half your mother’s and half of your father’s genes, and so too will each of your younger brothers and sisters. Therefore, you are as closely related to your full siblings as you are to your own offspring. Consequently, by sticking around and helping with the maternal and paternal chores you are potentially increasing the survival rate of your younger brothers and sisters and thereby nursing your own genes into subsequent generations.
Okay, so you’re not strictly getting your own genetic material into the next generation; but the genetic line, of which you are a part, is being maintained with your assistance. Obviously, there are factors that muddy the waters a little; relatedness is going to vary according to monogamy or polygamy, but you get the general idea. At this point, I feel I should point out that it is easy to disregard the above as a failure to acknowledge the emotions of animals. After all, do we think that foxes really count chromosomes? Of course not; foxes have no conception of chromosomes. This process marches on regardless, though. Why? Simply because it happens without the animal's input: it is entirely subconscious. The emotions that we identify as love and attraction are all ways our genes have of 'helping themselves' live on down the generations.
There are, of course, other good reasons for staying with your parents. Three heads are better than one when it comes to finding a meal, and strength in numbers can be a big bonus for ‘seeing off’ any potential assailants. Moreover, helpers may gain vital parenting skills and even inherit the territory from their parents. Still, not all dispersal is voluntary. Certain species won’t tolerate their weaned offspring loitering about; female deer will, for example, readily chase away any of their progeny still around by the following rutting season. Indeed, it has been suggested that, in some species (foxes, for example), helping provision food and babysitting may serve as a form of 'rent', allowing subordinate individuals to remain on their natal territory.