@Elizafox The other rule: the root is black, so you fix a red/red problem where the parent is the root by turning the root black. This is the only way to add black nodes - they rotate into the root. This happens when your rebalancing can't find a home for your extra red node so it makes it all the way to the root; all root-to-leaf paths are still "black equal" (because they were before you added a red node, your rotations don't change black depth, and your red node is red)...
@Elizafox the easiest way to make sense of it is to just pretend that the tree was fine before you added a node to it, and then you can fix it so it's okay again, and you don't have to worry about the rest. "the cool part" about red-black trees is how they figure out that they need to rebalance - the red-red rule is the only one necessary because it's the only rule that inserting a red node can break
