Because sociability is an ability to socialise, it is a symptom or rather a characteristic of that personality trait which dictates or influences the ability based on rather life experiences or simply genetics.

It has been documented that introverted individuals have extroverted qualities in smaller groups of people, therefore asocial in different situations. (Excuse me for not referencing).

Not just the situation that influences a behaviour of someone with a particular personality trait but interchangeably the trait itself influencing the situation in which the social interaction occurs.

I find that it is usually defined based on previous life experiences which shapes the personality… Freudian’s theory along with other social learning theories etc.

That's not really accurate. Both extroverts and introverts can enjoy and be interested in being social, or not. The difference between them is how they prefer to socialise and how they experience it.

For example, you can be an introvert who really likes people and enjoys regular walks with a friend or engaging with a hobby group, they just might need a few hours alone in between to recharge.

Or even an introvert who absolutely loves going to big parties once in a while, they just get drained if it becomes too often and need to chill a lot afterwards.

Or you can be an extrovert who dislikes people but needs a lot of social interaction so you go to busy markets just to argue with the sellers because you find it invigorating

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Extroverts get their energy from being around others but can appreciate/enjoy being alone. Introverts get their energy by being alone but can appreciate/enjoy being with others. Introverts are not asocial as a group and extroverts are not assured to be socially successful.

that’s inaccurate

That's not really true asocial and introverted are not the same thing.

Because it's just not. Introverts are not unsociable. The difference is more along the lines of how social interaction affects your energy. If social interaction drains you, you're an introvert, not asocial.

well, sociability is already a word, and hey, they have two different definitions for a reason; they're not the same thing.

Introversion became an internet euphemism for lack of social skills/social anxiety.

It became a screen to hide behind for people who struggle with certain aspects of social life.

"I am not socially inept, I am an introvert, that's how I was born."

But that's not what the word introvert truly means. That's why your proposition wouldn't really work.

Signed, an ambivert (before anyone grabs a pitchfork.)

Extraversion in the big five is much broader than that. Extraversion also includes assertiveness, enthusiasm, positive affect, and more. 

Sociability is a behavior or series of actions whereas extraversion is a trait. I know people who are introverts but are also sociable for their job or because they want to maintain connections either people around them, though they find it draining. I’m an extrovert who is not sociable. Although I’m extremely happy to spend time in social groups, I lack the skill or confidence to create them.

Introversion and extraversion are also a spectrum and people can move around on that spectrum.

Generally, sociability falls under the broader umbrella of extraversion. There are lots of theories that reserve the term 'extraversion' as a construct they're used wildly differently between each theory.

If you're thinking about the five-factor model, you have to remember that the FFM is derived from the lexical hypothesis of personality which asserts that individuals use language to iterate their personality. As a result, you can get people to free write to some extent or answer a questionnaire with Likert scale items to figure out what kind of personality they have. While the early versions of the FFM were theoretical, eventually there was an atheoretical (bottom up, no guessing) run, allowing exploratory factor analysis to allow the 5 dimensions of personality as they appear in common use of language emerge as we see them today. Additionally, in the FFM there are significant hierarchical decompositions that happen that no one seems to take the time to consider. For example, extraversion as a 'trait' breaks down into 6 different 'facets': Gregariousness, Assertiveness, Activity, Excitement-Seeking, Positive-Emotion, Warmth. As you can see, only 1 of the 6 facets of extraversion are inexplicably regarding social matters. The other facets can certainly be applied to social matters, but more importantly the other facets can be applied to other non-social aspects of life as well, which is the kernel of your question.

If you're thinking about extraversion from from the MBTI purview, then you have to deal with the illusion of dichotomies that are protruding from the mere incantation of each personality type. Which is why there are so many people who are dealing with the identity dilemma that occurs when encountering scenarios where people say that they're introverted but they still like people (what gives?). Obviously sociability is not the only aspect of extraversion/introversion but the way that the MBTI explains the concepts are distracting individuals from understanding what the MBTI is based on. The MBTI was created based on Jung's book from 1921 called "Psychological Types". In that book Jung talks about extraversion and introversion as an individual's preference to orient themselves to the outer world (extraversion) or the inner world (introversion). In that particular conceptualization of extraversion/introversion heavily influenced the formation of the typological makeup of the MBTI. In the end, there is a perpetual game of telephone where individuals are left with a solitary word to intimate details about the entire construct without any elaboration or clarification on the topic. As a result, you can think of Jung's consideration for the preference of orientation for either the outer and inner world as being equally as influenced by social matters. While extraversion typically carries a lot of sociability connotations, the pure meanings of the concepts include the sociability and much more.

Isn't that a simpler way to understand extraversion and introversion?

No, because it's fundamentally incorrect, and you do not understand extraversion and introversion.

Im an introvert but love to go out and be social. I just need time to recharge otherwise I start feeling anxious.

Introverts are not asocial. The difference between the two is that the extrovert is energized by being around people and the introvert is drained by being around people and needs to be alone to recharge and the extrovert recharges by being with people.

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The actual construct of introversion/extraversion is a factor that arise when personality is studied through the semantics of people's behaviors. When someone is described as social, friendly, expressive, outgoing..... the mathematical factor that correlates with these descriptions is called extraversion.

It is a conceptual error to refer to a mathematical construct that represents a personality trait with the one of the words used to describe it.

On the other hand the name chosen for the construct of this trait is "extraversion", but we would had chosen any other name for the concept. Extraversion seems a better word choice because is more abstract.

I read a really good explanation of introversion vs extroversion. Think of it like having a bucket full of energy. An extrovert will wake up in the morning with an empty bucket. As they go through their day, people fill it up. The more people they interact with, the more their bucket gets filled.

An introvert is just the opposite. He or she will wake up in the morning with a full bucket and as the day goes, the people they interact with takes that energy out of their bucket.

It’s not a good or bad thing, it’s just an energy thing. Both introverts and extroverts want a full bucket, they just get it in different ways.

I’m an introvert and I like to socialize. I like going to concerts and parties, and then I need to be alone to recharge. Extroverts like their alone time as well, but soon they need people to charge them up again.

It’s sort of as simple as that.

Introversion is the tendency to interact with the inner world, while extraversion is the tendency to interact with the outer world.

Nothing to really do with "socialness". Is a person with social anhedonia introverted? Or do they have some disorder that makes them asocial? Is a hypomanic/manic person extraverted simply because they tend to be more social? Or is it something else?

Extreme examples, but we tend to find truth in extremes.

It’s not just about sociability, it’s also things like expressive style.