Ah. They can grow up together.
Well, not really. By the time the average child is no longer doing Winston Churchill impersonations the kitten has grown up and, unless Measures have been Taken, has a family of its own. Kittens and children get on like a house on fire—and just think about what it's actually like in a house on fire…
A Real kitten in a Real household with a junior member can expect to be:
1) pulled
2) pushed
3) imprisoned in Cindy's bedroom with Cindy, Mr T in one of Cindy's dresses16, a one-armed teddy bear, a fearsome Madeofplasticoid with Lazer-zap cannon and a small pink pony
4) fed unsuitable food. In this category can be included peas, ghastly sweet pink goo, and a fortnight's worth of Kittytreats in three minutes
5) inserted into unsuitable clothing (cf. Cindy, Barbie, Action Man, etc).
6) carried around by being held in the middle, so that large amounts of cat flop down on either side. (Strangely enough, most cats put up with this, even when they are great fat neutered toms. It's like all that business with unicorns. Only young maidens can get away with it. The rest of us need stitches.)
It's not that children and young animals get along especially well. It's just that young animals aren't experienced enough to know what's going to happen. Stick to puppies. They're practically childproof.