Warning: This post contains spoilers for 'The Cursed Child'.
I wasn't surprised when Albus wasn't sorted into Gryffindor - this is a twist we probably all saw coming, because it would be pretty boring if all three of Harry and Ginny Potter's children ended up in the house everyone is familiar with by now. We've spent (almost) seven years in the Gryffindor common room, so Rowling, Thorne and Tiffany obviously saw the opportunity to change things around and venture into a new house in Hogwarts.
Whilst we don't actually spend much time in their living quarters, we do get a greater understanding of the students within Slytherin as Albus Potter and Scorpius Malfoy guide the way for the eighth story in the series - they don't live up to the reputation former students of their house have built up for them, and this really makes up for - what I think was - a poor representation of Slytherin house, told through Harry Potter's unreliable narration throughout the seven books.
Is it a surprise that Harry had such a hostile opinion of Slytherin house? No, of course not; he didn't exactly have great personal experience with their members. But, The Cursed Child gave a necessary insight into the minds of Slytherin students, and allows those who perhaps don't have such a high opinion of the house to understand that they do actually have some redeeming features.
First of all, I have something to confess: I'm a Slytherin. Second confession: when I was first sorted into Slytherin, I wasn't happy about it. After reading and watching Harry Potter for years, finding out I was part of the asshole house wasn't exactly a happy revelation for me. I was quickly cheered up about it by my brother, who told me "well, it could be worse, you could be a Hufflepuff".
Now, I'm not saying that Hufflepuff is a crappy house, because that would make me an asshole, but whilst that comment was a harsh jab at the Hufflepuffs, it did set me on a path to becoming a proud Slytherin - because, whilst it does have the most obvious flaws out of all the houses, it doesn't try to hide them. Partly because it is very difficult to hide them (kind of hard to ignore all those Death Eaters), but also partly because, as the Pottermore Wikia puts it:
members are not afraid to admit [its flaws] as one of the Slytherin traits is ambition and greatness.
So of course, as a result of that ambitiousness and greatness, you're going to get some (really, really) bad apples in the mix. It's a risk all of the Hogwarts students have, regardless of what house they're in. Unfortunately, a lot of extremists came from Slytherin; is that something we're proud of? No, obviously not. But we're not going to ignore what happened, because in order to prevent history from repeating itself, we have to accept what happened and change it for the better. That really gives Slytherin house a sense of wisdom that even Ravenclaws would be jealous of.
One particularly important example of a Slytherin defying the expectations of their house is, of course, Severus Snape. Because of the negative preconceptions we've developed about Slytherin, we assume that Snape's harsh treatment of Harry is firstly because he comes from a house full of awful people, and secondly because we assume he's just another Death Eater out to stop the hero of the story from fulfilling his destiny.
But, as the series moves along, we see that Snape is a truly loyal friend of Dumbledore's, who risks his life to make sure that Harry does indeed fulfill his destiny. His bitter attitude towards Harry came as a result of being reminded of the life he never had with the woman he loved, Lily Potter. Whether you feel as though Snape's hostility towards Harry is justified or not, without his role as a double agent, the wizarding world probably wouldn't be the same - and there should be no doubt that his actions were a force for good.
What I particularly loved about The Cursed Child was that it didn't paint Slytherin students in the typically arrogant way we know they're infamous for; we see two boys a part of that house rejected by their peers because of the legacies their fathers have left at Hogwarts. Albus is seen as a disappointment to the Potter name, partly because he was sorted into Slytherin and not Gryffindor; Scorpius is seen as maintaining the dark Malfoy reputation when sorted into the hated house.
The obvious theme in the The Cursed Child is children struggling to live up to their parents' legacies, but a slightly less obvious theme stemming off of this one is readdressing the Slytherin stereotype and showing how Albus and Scorpius use their cunning nature, resourcefulness, ambitiousness and fraternity to try and do a good thing for an old man - Amos Diggory.
While those who have read the script know this doesn't go to plan, and things do go very badly for the two friends, they do all they can to make things right again. When they fail the first time, they go back and try to rectify the situation. When things go really, really, really bad the second time around, Scorpius could have decided to stay in the world where Voldemort rules, and where everyone worships him and see the Malfoy name as one of the greatest there is. That world was a lot more beneficial to him than the one he knew was, and going by the selfishness Slytherins are expected to have, well, by staying there he would have just been living up to his house's reputation. But he didn't - he chose not to, because he valued his friendship with Albus more than his popularity. This was a great demonstration of that Slytherin fraternity, and really showed us the true nature of the house.
If we go way, way back to the beginning of the Harry Potter series, the Sorting Hat says this:
Or perhaps in Slytherin,
You'll make your real friends,
Those cunning folk use any means,
To achieve their ends.
Even from the start we're getting some fishy vibes from the green house, but if we look at this verse from a different perspective, they actually appear more selfless than selfish. Someone using any means to achieve their ends initially sounds highly self-centred and childish, but what if this is meant in a way where the ends the person wishes to achieve is to help someone else through a troubling time? That's exactly what Albus and Scorpius do in order to help Amos Diggory, and later on what they do in order to contact their parents from 1981.
From this, we see the boys use resourcefulness to both (accidentally) mess up the wizarding world and later save it from a grave threat, and as a result of their time-travelling journey, become far more considerate and mature people.
Albus starts of the story as stubborn and resentful of his father, and Scorpius starts off as meek and lost without his mother. But, through finding each other and forming a friendship great enough to match the golden trio's, they go on an adventure that starts off as one to change an old man's life for the better, and instead change their own lives by learning about their fathers'. Instead of being stubborn and resentful, and meek and lost, they become open-minded and understanding, confident and driven. That, in itself, demonstrates the true nature of a Slytherin - someone who makes the right friends, does all they can to help others and, as a result, grows positively as an individual.