Most dogs want to be with their person, and some are virtually glued to their human. We tend to give human traits to those around us, but it is important to understand that a dog following their person around isn't necessarily a sign of separation anxiety. It can be, but it doesn't have to be.
Our American Eskimo would follow me to the bathroom if I let him. He usually waits right outside the door, with his nose an inch or so away from the annoying barrier that separates him from me. He's okay with me leaving the house without him, he's not anxious, but he prefers to be by my side.
Humans are social beings, but dogs are much more so. We tend to balance our social lives with solitude for peace and quiet. Dogs have no concept of "alone time." Dogs want to be with their pack, which in modern society equals their human.