The reason why you don't stir caramel is to prevent crystallization as well as to ensure you get a smooth and silky texture to the caramel.
When you stir the caramel you can interrupt the chemical changes that take place which transform the sugar molecules into caramel, which leads to the formation of sugar crystals.
Although stirring of caramel is sometimes needed to ensure that all of the sugar dissolves before the caramelization process begins to take place.
Stirring of the caramel after the caramelization takes place causes agitation and causes sugar molecules to clump together and form crystals.
Stirring of the caramel can also push any undissolved sugar granules onto the sides of the pan, where they can cool and become hard and cause crystallization.
There are some exceptions to stirring caramel which includes dissolving of the sugar, adding ingredients and using the dry method.
When making caramel with the dry method, stirring can be used to ensure that even heating occurs and to prevent burning.
The dry method of caramel making is where the sugar is heated alone until the sugar melts and caramelizes.
And when making caramel, it's often necessary to stir the sugar and water initially to ensure that the sugar dissolves completely before the mixture comes to a boil.
And once the caramel is at it's desired stage, it's safe to stir the ingredients in such as butter, cream and flavorings.