Why are Hogwarts students threatened with expulsion so much?

Question

It seems to me that the threat of expulsion is hung over the heads of Hogwarts students pretty frequently during their time at the school. In Philosopher's Stone in particular the students seem constantly terrified that they might be chucked out. Being expelled has extreme consequences, as we see with Hagrid - your wand is snapped and you're consigned to a life on the confines of wizarding society. Even when allowing for Harry and co getting into trouble more often than the average Hogwarts student it seems to be mentioned a lot. Not only do the students themselves worry about being thrown out but the teachers too seem to actively threaten trouble-makers with expulsion on a regular basis.

However, from the examples we have from the books, only Hagrid is actually expelled - and that was for something very severe. (Fred and George arguably were expelled too but I'd argue that they jumped before they were pushed).

Why is expulsion frequently threatened but hardly ever enforced? Are the Hogwarts teachers just being mean and manipulative?

There are plentiful examples below, which I include for completeness's sake.

Examples of students worrying about being expelled:

A horrible thought struck Harry, as horrible thoughts always do when you're very nervous. What if he wasn't chosen at all? What if he just sat there with the hat over his eyes for ages, until Professor McGonagall jerked it off his head and said there had obviously been a mistake and he'd better get back on the train?
_{(Philosopher's Stone, Chapter 7, The Sorting Hat)}

Now he'd done it. He hadn't even lasted two weeks. He'd be packing his bags in ten minutes. What would the Dursleys say when he turned up on the doorstep?
_{(Philosopher's Stone, Chapter 9, The Midnight Duel)}

There was no reason on earth that Professor McGonagall would accept for their being out of bed and creeping around the school in the dead of night, let alone being up the tallest astronomy tower, which was out-of-bounds except for classes. Add Norbert and the Invisibility Cloak and they might as well be packing their bags already.
_{(Philosopher's Stone, Chapter 15, The Forbidden Forest)}

Example of the Ministry of Magic threatening expulsion:

The severity of this breach of the Decree for the Reasonable Restriction of Underage Socrcery has resulted in your explusion from Hogwarts School of Witchcraft and Wizardry. Ministry representatives will be calling at your place of residence shortly to destroy your wand.
_{(Order of the Phoenix, Chapter 2, A Peck of Owls)}

Examples of the teachers threatening expulsion:

Strict and clever, [Professor McGonagall] gave them a talking-to the moment they had sat down in her first class.
"Transfiguration is some of the most complex and dangerous magic you will learn at Hogwarts," she said. "Anyone messing around in my class will leave and not come back. You have been warned."
_{(Philosopher's Stone, Chapter 8, The Potion's Master)}

"None of you is to move while I take this boy to the hospital wing! You leave those brooms where they are or you'll be out of Hogwarts before you can say "Quidditch". Come on, dear."
_{(Philosopher's Stone, Chapter 9, The Midnight Duel)}

"Silence!" snapped Snape again. "Most unfortunately, you are not in my house and the decision to expel you does not rest with me. I shall go and fetch the people who do have that happy power. You will wait here."
_{(Chamber of Secrets, Chapter 5, The Whomping Willow)}

"I will be writing to both your families tonight. I must also warn you that if you do anything like this again, I will have no choice but to expel you."
_{(Chamber of Secrets, Chapter 5, The Whomping Willow)}

"Miss Granger, you are already facing suspension from this school," Snape spat. "You, Potter and Weasley are out-of-bounds, in the company of a convicted murderer and a werewolf."
_{(Prisoner of Azkaban, Chapter 19, The Servant of Lord Voldemort)}

Harry had already been called out of the common room to endure fifteen highly unpleasant minutes in the company of Professor McGonagall, who had told him he was lucky not to have been expelled and that she supported whole-heartedly Snape's punishment of detention every Saturday until the end of term.
_{(Half-Blood Prince, Chapter 24, Sectumsempra)}

Answer 1

PART 1: One must look at the situations Harry and Co. were putting themselves in... normal students were not getting into the type of "adventures" that the trio was.

To go through your examples:

1. Sorting Hat - It is Harry's first experience at the school. He has no idea of how Sorting works. His greatest fear is being sent back to the Dursleys'.
2. Midnight Duel - Harry is only in the second week of school and already breaking rules by arranging to duel underage student. I don't know about you, but my school expelled students who got into fights.
3. Forbidden Forest - Objectively, a student has broken at least three separate rules, having an illegal creature, and having a magical item of unknown properties. Suspension is a valid concern in this instance!
4. A Peck of Owls - Harry had "clearly broken" the International Statue of Secrecy. He had broken not a school rule, but a law. He would be expelled and not even be able to practice magic.
5. Transfiguration Class - There is no threat of expulsion here, only not being able to learn Transfiguration. As this is a highly dangerous subject, this is not unreasonable.
6. Quidditch - Hooch was exaggerating just a bit. She did not want any unsupervised flying attempts. One student was already injured, she did not want to risk another.
7. Whomping Willow - Ron and Harry had stolen an unregistered magical item and most likely broken the International Statute of Secrecy. Upon arriving at school (as Snape makes clear) they crashed into the Whomping Willow and nearly destroyed it. Again, breaking laws and destroying property is really something to be concerned about!
8. See above...
9. Shrieking Shack - Breaking multiple school rules and AIDING AND ABETTING a known CRIMINAL! They are probably lucky Azkaban wasn't being mentioned!
10. Sectumsempra - Harry nearly kills Draco. If Snape had not been there and recognized what had happened it is conceivable for Harry to be tried for murder. Expulsion and Azkaban would seem likely.

Recap - Harry, Hermione, and Ron are in situations beyond what would be expected from "normal" students. The threat and fear of expulsion (if not worse) in almost all cases is justified.

---

---

PART 2: Expulsion from Hogwarts is rarely enforced because it would essentially ostracize you from the entire Wizarding World. (Note I am not taking into consideration that Newt Scamander was expelled, since FB was published later.)

The only expulsion we see from Hogwarts is Rubeus Hagrid. Once expelled, his wand was also snapped, because without completing his education the governing bodies have deemed it unsafe to practice untrained magic. Hagrid is also a special case because the reason for his expulsion is also related to the death of a student. Not being able to use a wand is going to severely limit Hagrid's job opportunities. Dumbledore was gracious enough (and knew Hagrid was innocent) to employ Hagrid as the groundskeeper at Hogwarts.

In general, those who cannot perform magic are not treated very nicely within the magic community. Look at the two confirmed Squibs: Filch and Mrs. Figg. Both are not thought of very highly by anyone, except again Dumbledore.

In the specific case of Harry Potter:

1. Prior to OotP he is "The Boy Who Lived"! Let's be honest, teachers are going to give him the benefit of the doubt. Even more so since they realized he had no clue about what he was.
2. OotP and beyond: Harry was indeed expelled over the summer after the Dementor Attack... However, even that could not stick as he still had the support of the majority of wizards (that and the charges were nonsense).

Recap: Expulsion is rarely used because of how detrimental it would be to the entire life of a Witch or Wizard.