Why are rockets stable?

Here's my question: Why are rockets stable? If I try to balance a pencil or a broomstick on my finger, it takes a lot of movement to keep the pencil/broomstick balanced. But rockets, from the space shuttle to model rockets to water rockets, take off without problems. At speed, the fins may help to direct the rocket, but when the rocket first launches, why don't they all spin out of control? It seems that rockets are inherently stable which seems to be counterintuitive. Why? How do rockets seem to work consistently without problems. I know that rockets like the shuttle have engines that can move to direct the thrust that may help. But my model rockets from my childhood had no such controls, nor do water / compressed air rockets. Does it have something to do with the momentum of the jet of fluid leaving the motor? Come to think of it, if I have a hose with a nozzle on it and let it go , the end moves around randomly without control. Exactly the opposite of a rocket. Charles I Moore