Plain Lantern 
Most of us have done it. Closed a book with a lump in the throat over someone who does not exist, or felt genuinely flat for a day or two after finishing a long series, as though a friend had moved abroad. It is a faintly absurd thing to admit. You are mourning a person made of ink and paper, invented by a stranger. And yet the feeling is real, and nearly every reader knows it.
So why do we get so attached to people who were never actually there? It turns out there are good reasons for it, and none of them mean anything is wrong with you.
We are built for other minds
Human beings spend their whole lives working out what other people are thinking. It is how we rub along together, and our brains are very good at it. A well-drawn character gives all that machinery something to do. You infer their motives, predict their choices, brace for the mistake you can see coming. As far as the reading part of your mind is concerned, you are getting to know a person, and it does not keep a careful line between the real ones and the invented ones.
You know them better than you know most people
Think how little you actually see of even close friends. You get their surface, their good behaviour, the version they have decided to show you. A character you follow the other way, inward. You hear the things they would never say aloud, watch them at their worst, and understand exactly why they did the thing everyone else in the story judges them for. That is a depth of access you almost never get with a living person, and it breeds a strange, one-sided closeness.
Psychologists have a name for these bonds with people we never actually meet. They call them parasocial relationships, and the research suggests they lean on much the same wiring as our real ones.
They are relationships with nothing at stake
Part of the pull is simple safety. A fictional friend cannot let you down at an awkward moment, cannot judge you, cannot need anything back from you. You can care about a character completely and lose nothing by it. For a shy reader, or anyone going through a lonely stretch, that undemanding company is a genuine comfort, and there is nothing to be embarrassed about in taking it.
It is empathy, quietly practising
There is decent evidence that people who read a lot of fiction get some practice at understanding others, since that is more or less what the reading asks of them. Every time you slip into a character unlike yourself, agree with them, argue with them, forgive them, you are stretching the same muscle you use on real people. Getting attached to a character is that muscle at work, not a lapse in judgement.
Some of them shape us
A few characters do more than keep us company. They leave a mark. A reader might carry a fictional person's steadiness, or their courage, or their dry way of facing trouble, and quietly borrow it in their own life. Ask someone about a character who mattered to them at fifteen and you often hear less about the plot than about who they were trying to become at the time. The attachment was part of working out what kind of person to be.
Which is why the last page hurts
All of which explains the small grief at the end of a good book. You have spent real hours with someone, learned them, come to care, and then the pages simply run out and they carry on without you, frozen at the point where you left them. Missing them afterwards is just the cost of having let them matter in the first place.
If you would like the kind of book that gives you people worth getting attached to, calm and well told, you are welcome to browse the Plain Lantern library. A character who stays with you long after the last page is one of the better things a book can hand you.