This is the biggest factor of all. Some people come out of high school or university unsatisfied with how their social lives have gone so far. They look back and are bummed out that they didn't have many friends, or that they haven't had a relationship yet, or that they didn't get to take part in all the usual experiences people their age seemed to be having. High school and college are important, but when you're done with them you're still relatively young. Many people start to get the hang of socializing in the years after graduating, just because they have more time to practice and figure things out on their own.
A lot of people seem to go through a natural trajectory where they're really awkward and shy in high school, a lot better, but still struggling somewhat in college, and then by their mid-twenties they've gotten past the worst of it. There was nothing intrinsically wrong with them when they were younger. They just needed a little more time to pick up the concepts, learn to work around a naturally shy personality, and to catch up with everyone after getting a late start.
Personally I notice this in people who have stereotypically awkward professions, like working as a computer programmer. It doesn't apply to every last person, but I'd say it's not totally unreasonable to claim that teenagers who are into programming are a bit more socially awkward as a group. I've met many middle-aged guys in the technology field and most of them are as socially adjusted as anyone else. By that time they've had years and years to grow out of any bad habits they might have had.
When you're younger you just haven't had enough time to develop a range of interests. I think people more easily fit into stereotypes when they're in high school simply because of they haven't had a chance to move beyond the handful of things they naturally got interested in first. As people get older they've had the time to pick up additional hobbies and flesh out their personality. They can even accidentally get into pastimes they never would have guessed they'd enjoy one day. Of course, the more interests you have, the easier of a time you'll have relating to people and making conversation with them. You'll also be able to do more things with your friends (e.g., you can go mountain biking with them, instead of bowing out and telling them you'll only meet them for dinner later).
Many people have personalities, interests, or appearances that go against what society says are the 'right' ones to have. When they're younger they can feel really conflicted about this. Following their natural dispositions seems to make them the happiest, but they may also take society's messages to heart and tell themselves things like, "I'm such a loser for being into anime. Why can't I just like cars and golf and whatever and be a normal person?"
As people age they tend to make peace with the ways that they're different. They learn to be more sure of themselves and not be too swayed by what everyone else thinks. They decide there's nothing wrong with being how they are, and that some people will like it and others won't, and that they can handle that. Some people aren't even that old before they develop that mentality. Practically, this means they act and feel more quietly confident, and they no longer hesitate to seek out the type of social life that works best for them (e.g., only having a few friends, skipping on rowdy parties, being unembarrassed about joining a tabletop gaming club).
This isn't to say that once someone becomes comfortable with themselves they rigidly lock their personality down for all time. You can still be open to changing or developing new facets of yourself. You can still identify traits that you want to improve upon. But you don't beat yourself up just because you want to spend a Saturday morning reading a fantasy novel.
In high school and college you're more restricted in who you can spend time with. I don't even mean stereotypical movie stuff like how a Prep can't hang out with a Goth. When you're younger there's an unwritten expectation that you're going to be friends with people close to your own age. But if someone is twenty eight there's nothing stopping them from hanging out with their 45-year-old co-worker, or the 37-year-old guy they play poker with. It's okay to have a wider range of friends, and once you're out in the world you get exposed to a broader group of people.
Sometimes people will tell you that they don't have a ton of friends because they feel like they just don't have much in common with their similar-age peers. When you get older this doesn't hold you back as much. If you feel like you want to hang around more experienced, mature people, or a very specific variety of person, then you can go find them.
Anyone will seem more awkward and out of place if they're plopped in an environment that's not a good fit for them and doesn't value what they're about. When you're younger you're stuck wherever your parents chose to live. If someone goes to university, they don't always have a ton of options about what school to go to either.
When people get older and gain more independence and money they get more say about what kind of environment they want to be in. Some people come across as "late bloomers" not because they totally changed, but because they were finally able to put themselves in a situation where their true selves could blossom. They can get out of their small, boring town and move to a new city that's filled with their type of people. They can choose a job that plays to their strengths and style of socializing. They may live in an area that's not for them, but buy a car and easily be able to drive somewhere better on the weekends. If they prefer living alone they can afford to get their own place.
Everyone knows that kids and teenagers can be really nasty to each other. I don't want to oversimplify things and say adults are never mean-spirited or abusive. They are. They can also be jerks to each other in much more subtle, insidious ways. But in general adults are nicer and more tolerant in the face of social awkwardness. If a young girl is acting a bit shy her classmates could very well make fun of her to her face. An adult is more likely to be polite, patient, understanding, and accommodating. They may try to subtly include or help someone who's being quiet at a party. Especially in certain workplace environments, people are a lot more behaved. Even if an adult is put off by someone who's socially awkward, they're more likely to just bite their tongue and stay out of the person's way, rather than try to make their lives miserable.
In a lot of ways, this all creates an atmosphere where it's easier and safer for someone who struggles with social skills to be themselves, and to work through their issues. Yeah, not everything will be perfect. For example, if a person tries to invite someone out who's not interested, they may still get a 'polite' run around. But at least they can be pretty sure they won't be openly mocked for asking the wrong person to see a concert with them.
This is a bit related to the idea of people not being jerks. When you're in high school a diverse group of people are all forced to be in close proximity to each other. Even when you want to tell yourself you shouldn't care what everyone else is doing, you can't help but know anyway, and get sucked into it to a degree. This is way less of a problem in college, and almost totally goes away after that. When you're older you have way more freedom to do your own thing and not get a hard time for it. For one, people can't practically follow what you do. They're also busy with their own lives and have better things to do than worry about how someone else spends their days.
For example, if you've done well in your career that can give you a sense of self-worth that you can bring to your conversations ("Who cares what this guy thinks of me? Even if he doesn't like me it doesn't change the fact that I've accomplished X,Y,Z." As a teenager or college student you may not have these achievements to draw on (though none of this is to say that if you don't have a bunch of points to put on a resume that you can't feel confident).
As you've gotten older you've likely built up useful skills and habits that can also help you socially. They could be broadly useful ones like self-discipline, tolerance for discomfort and uncertainty, being able to think long term, or being able to resist getting sucked into pointless arguments. It's easy to see how some of those would help you get out there to practice and not give up too easily. The skills could also be more practical and open up more opportunities (e.g., knowing how to cook, so you can throw dinner parties for your friends; knowing how to drive so you can go to events in neighboring towns).
I know I painted a pretty positive picture above, and I think those factors are more powerful than the ones below. Most of the points in this section share a common theme of it being harder to meet people. None of this is to say that it's impossible to make friends when you're older, but I'd say it is a little trickier. The things I mention below are fairly common complaints that people have made.
I think it starts to happen at a different age for everyone, but there will be a stage when you notice that the people in your life just don't have as much free time to hang out anymore. They're too busy with their jobs, partners, and families. If you're trying to make new friends, or keep a friendship going, this can really get in the way. It's not enough to meet someone you get along with, they also have to have enough breaks in their schedule to hang out with you. Not that easy when they have to work on the house, drive their kids to soccer tournaments, and visit their in-laws every weekend. Not to mention, you may be just as busy with the same kinds of things yourself.
Besides having to compete with people's hectic schedules, a lot of the potential friends you meet when you're a bit older may already have well-established social circles, which gives them little motivation to seek out someone new. You may meet someone you get along with at work, but when they do get time off from their family, they go away for the weekend with a bunch of friends they've known since grad school. It can be really tough to break into a group who have twenty years of shared experiences between them.
In high school and college everyone is obviously at the same school. Many of the people you meet also live fairly close by. In university it's not hard at all to gather up ten people on a Friday night. When you're older your friends can be all over the place. One person could live in the suburbs half an hour north of the city. Another could live in a feeder community an hour to the west of it. These little things make it that much harder to organize get togethers, or to hang out spontaneously.
I already hinted at this in the previous section, where I talked about how people are less likely to be jerks, or to care what you do. Sometimes this tactfulness goes a bit too far and can leave older people who still struggle with their social skills really lost and frustrated. A middle-aged person may not have as many problems as they did in college, but still have things they want to work on. However, they can't seem to get anywhere with anyone. They know they're not having the success they want. They assume they must be doing something wrong, but no one will give them any clue about what it may be.
Everyone just seems to quietly exclude them. They try to invite people out, but are met with walls of friendly, reasonable excuses. There's a social life going on at the office, but they're on the outside looking in. Other people have their own stuff going on and aren't going to take it upon themselves to try to help them out. Even if they want some direct feedback, everyone is too nice to offer it. At least in high school someone might get annoyed and tell them, "Ugh, you're so desperate and needy! And you wear the same cloths every day!" That's mean, but at least it's something to go on.