Why does my cat follow me into the bathroom and sit there staring? It is the one room she insists on.

Question 2 has a neat answer: the kitchen is where the food is, and that is precisely why it is less special.

You go to the kitchen many times a day, at unpredictable moments, and she can get your attention there any time she likes. There is no scarcity. The bathroom is a limited-availability, high-attention window with a known start and end.

There is also a plainer version: in the kitchen you are usually doing something with your hands and moving about. In the bathroom you are as close to a stationary lap as you ever get outside the sofa.

Cats optimise for access to their person, not for proximity to food, once food is reliably available. This is the same reason a cat will ignore a full bowl to sit on the newspaper you are reading.

There is a real explanation and it has several strands that all point the same way, which is why the behaviour is so consistent across cats.

You are stationary and predictable. Most of the day you move around unpredictably and are hard to be near. In the bathroom you sit still, in one place, for a known length of time. For an animal that likes proximity on its own terms, that is the best available window.

It is a small, enclosed, hard-surfaced room with one entrance. Cats favour spaces where they can see the approach and nothing can come from behind. Bathrooms are, architecturally, close to an ideal cat spot.

Water. Running taps, condensation, a bath, a shower - a room that regularly produces fresh moving water is genuinely interesting to a species that prefers running water to a bowl.

Scent. It is one of the strongest-smelling rooms in the house in cat terms, and much of that smell is you.

So it is not one thing. It is the room where four separate preferences happen to coincide.

The closed-door part is a different behaviour and worth separating, because it generalises.

What cats object to is not the room, it is the barrier and the loss of information. A cat that has never once entered your study will still complain at the study door if it is closed, and lose interest the moment it is opened, often without going in. The interest is in access, not the destination.

So the bathroom gets a double dose: it is the room she wants to be in and it is the room where the door actually gets shut. Every other room is open, so the behaviour never appears there and you never notice it.

A cheap test if you are curious: shut a different door for a week. Most people find the complaining follows the door rather than staying with the bathroom.

On "she does not do it to guests": that is the part that tells you this is a social bond rather than a room preference.

Following behaviour is directed at the person the cat is attached to. Guests are not that person, and are also not predictable enough to be worth following.

Worth mentioning only because people sometimes worry that following is anxiety. Attachment-following looks relaxed: she arrives, settles, may groom or doze. Anxious following looks different, pacing, vocalising, not settling, and it happens everywhere rather than in one room. From your description, yours is the first kind.