Are kittens and puppies adopted over adult cats and dogs or is that just a rumor? If so what leads them to this choice? Is it just because they are cuter?
Yes, puppies and kittens get adopted much faster than older dogs and cats. I've worked at an animal shelter every weekend for almost 6 years. Puppies go the fastest because we have less of them and you can tell their breed easier than kittens.
We have one of the fastest adoption rates in the country (US): 17 days. Puppies and kittens can go within the hour we put them out. Adult dogs and cats can take a month or two to be adopted. Other shelters aren't so lucky.
I listen to people's reasoning for adopting a puppy or kitten. I hear things like, "I want my kitten or puppy to grow up with my kids." "My child wants the kitten or puppy." "She\he is so cute. I can't stand it. I have to have her/him". Mostly these decisions are emotionally-based or uneducated.
We try to educate adopters on how difficult a new puppy or kitten will be. And of course my favorite thing to say (jokingly, but not) is..."you know they grow up, right?"
Unfortunately, this is true.
Cuteness is part of it. Wanting to feel that the animal is clearly "yours" plays a part. Some folks are afraid that the animal was surrendered due to behavioral problems and don't want to risk adopting someone else's training mistakes. Some folks don't want to give up more years of living with the animal than they must.
And so on. Different people have different concerns. But there are enough people with some concern to make this statistic exist.