I don't get the Monstrosity creature type at all. There are some things in it that are obviously monstrous, like the dragonflesh grafters, but then there are things like rocs, which are just REALLY giant birds. I feel like a lot of the things in the Monstrosity type could just be made beasts, such as owlbears and even remorhazes. Why is a stirge, which looks like an amalgamation of bat and mosquito, a beast, but a purple worm, which is just a big worm, is a Monstrosity? There are so many animals in real life that are just as weird and creepy as stuff like carrion crawlers and ankhegs. Even the new dinosaurs from Bigby Presents: Glory of the Giants are Monstrosities, when all other dinosaurs are beasts. Or in Spelljammer, where asteroid spiders are monstrosities but all the space fish are beasts? It doesn't make sense to me, and it feels like it limits options for the polymorph spell and for moon druids. Does anyone have insight on why so many different things are Monstrosities?

I think monstrosities mean creatures that aren't normal everyday creatures where they come from, underdark things, smart beastlike things, or hybrids. Now, stirge are creatures that look like hybrids, but it is not confirmed if they are. Chimera, they are a hybrid, and rocs, you don't see them where they live constantly. Carrion crawlers are from the underdark. If a hook horror with out the underdark, it would be a beast, cuz it isn't a hybrid

It's always "what is a monstrosity? why is a monstrosity?" and never "how is a monstrosity?" :(

Some guidance can be found in the description of the different creature types in the Monster Manual. The 2024 version says:

Monstrosities are unnatural creatures with strange origins, such as mimics and owlbears.

The key there, I think, is the "strange origin" part, and the older 2014 version of the monster manual is even more explicit about this:

Monstrosities are monsters in the strictest sense — frightening creatures that are not ordinary, not truly natural, and almost never benign. Some are the results of magical experimentation gone awry (such as owlbears), and others are the product of terrible curses (including minotaurs and yuan-ti). They defy categorization, and in some sense serve as a catch-all category for creatures that don’t fit into any other type.

So I think the key distinction between monstrosities and beasts is at least in part that beasts have a natural origin (despite many of them not existing in real life) while monstrosities have an unnatural origin. 

That said, there are still some things that don't fit this pattern (e.g. asteroid spider is described as being of natural origin) which may be down to different writers conceptualizing things differently. There may also be a desire to not make some things Beasts in particular specifically to prevent Druids from being able to turn into them for game balance reasons.

I think Monstrosities are unnatural creatures that don't fit other creature types but otherwise vary widely 

Quote from wagnarokkr >>

There may also be a desire to not make some things Beasts in particular specifically to prevent Druids from being able to turn into them for game balance reasons.

 This is likely the real difference. Having a class of "normal" critters that the players can't tame/summon/change into, without the inherent mechanical interactions that many of the other creature classes bring.

They were talking about the category in the Monster Manual pre-release video New Monstrosities | 2024. They started explaining the category, but also went into the reason for moving werecreatures from humanoids to monstrosities:

[...] before we dive in there I think just for people are wondering what the heck is this category [...] the monstrosity category is the category for classic monsters, the chimera, the hydra, things that you know in the storybook, it's not a dragon specifically, or one of the other very distinctive creature types, that classic monster is a monstrosity, and one of the few things that unites them is many of them were either crafted or distorted by magic, so as you go through you'll see that often the one thread that they have in common is like [...] with the owlbear was you know a wizard did it, or this used to be another type of creature but because of a curse, plunging into this other plane of existence or something else, it became this other creature [...] or mythical creatures like the guardians of the gods [...] this is the category for medusas, for hydras, for basilisks, like those sort of mythological creatures things that are animals with the special abilities that are mashups of creatures something that could be a real creature but just from some place you haven't been before [...] And with that in mind [...] this is the category of monster that was shaped by magic whether the magic of the gods or the magic of a mortal or somehow mutated by magic. That is one of the big reasons why we moved werecreatures into this category. We previously had them as humanoids and [...] we reconsidered the creature types of everything in the monster manual we realized that was a funny choice because the creatures all started as humanoids but they're not humanoids anymore. And we did that not only for story reasons but for mechanical reasons because there are a number of things in the game that specifically affect only humanoids and we did not want those things affecting werecreatures, because part of what's special about them is they're now strange, they're other part of often a lot of classic werecreature stories, it's one of the first hints that something is off is the person might look human or some other type of humanoid but things are weird around them [...] so they now are in this category and they have all been redesigned. One of the big changes for all of the werecreatures is the curse that they apply is now inside each step block [...]