Pragmatic Motivations People Have For Improving Their Social Skills
Many people don't have the most polished social skills or the most popular interests. They're fine with that and aren't motivated to do things differently. In a perfect world they could be as they are and not have to go through the hassle of changing. However, many of them do end up working to acheive "good" social skills in society's eyes. Or they take on new hobbies to try to get along with people more easily.
The reason they change and conform isn't because they're intrinsically motivated to do so. They're being practical, they want a payoff, and they feel changing their people skills or expanding their interests is worth the sacrifice. Here are some outside forces that compel people to change:
Relationships and sex
This one is particularly true for heterosexual men. Societal roles being what they are, if they want a relationship or someone to hook up with they have to be proactive about going after it. There are plenty of men out there who have little to no interest in socializing, and who aren't very practiced at it. They have esoteric or stereotypically dorky interests. They're also totally comfortable with all this and aren't concerned with what people think of them. If they had magical powers that would let them effortlessly get a girlfriend, they wouldn't change at all.
Of course, they don't have those fantasy powers, and they're drawn to the opposite sex. Maybe they want a partner, or something more casual. Either way, it's a huge motivator. What happens with some of these guys is that they first approach the issue with the mentality of, "I want to be true to myself. I want to meet someone in a way where I can be myself and not have to change." Sounds reasonable enough.
So they try that and hit a wall. Their social skills are just too unpolished to attract the kinds of women they're interested in, if they have the guts to approach them at all. They don't know how to put their best foot forward. There aren't that many women who only want to talk about the obscure topics they've learned a lot about. Many of them aren't into guys who know nothing about how to dress themselves. You know that ideal, that there's someone out there for everyone? Well, sure, maybe there is, but if these men stuck with their current "I won't change" plan it may take them seven years to find that person.
Following the giant carrot that is being able to get a girlfriend or have sex, some of these guys realize their old approach just isn't working, and start taking steps to improve their social skills. They wouldn't be motivated to do these things for anybody else, but for women they will. They learn how to be more natural conversationalists. They improve their wardrobes. They take up some new, more relatable hobbies so they can chat to people more easily. They may even do the cliche thing and take up some hobby that's supposedly attractive to women, like playing the guitar. Whatever they think it will take.
To help a cause that's important enough
If someone believes in a cause strongly enough they may be willing to work on aspects of their social skills they wouldn't much care about otherwise. For example, someone may improve their public speaking, schmoozing, or persuasion abilities so they can promote a charity. A woman who normally likes more low key get togethers may be willing to attend and work the room at a noisy fundraising party for a non-profit she supports.
To avoid rejection and hassles
Even if we say otherwise, it's very hard not to care what people think of us. We're wired to be sensitive to criticism and rejection. For some people this is painful enough that they'll improve their social skills just so they won't be singled out and picked on any more. I think everyone does this to at least some degree. I'm not claiming it's always good that shame and peer pressure can motivate people to change. I'm just pointing out it happens.
Money, career advancement or stability
People also frequently make social compromises for their careers. They do it for financial security, to not get fired, to climb the corporate ladder, or because they like what they do and want to hold onto it.
In some cases someone will have to acquire certain social skills to do their job effectively. Think of an employee in sales, or customer service, or who works mainly for tips, or a manager whose department will fall apart if she isn't an effective leader. The other big reason is that office cultures often expect people to be sociable "team players". Employees will get criticized on their performance reviews for being too private or withdrawn. In a lot of workplaces the ideal co-worker is a chatty social butterfly who's trying to get everyone to join the office fantasy basketball pool. So in order to keep their job, or have a shot of becoming manager, or to just get their fellow employees off their backs, some people will try and become more sociable at work.
More or different friends
Most people can find a niche that jives well with their natural tendencies. At times someone will be more-or-less satisfied with their default social circle, but also want a little bit more. Maybe they'd like a greater number of friends than they'd naturally attract, or they want some things that only a different type of buddy would give them access to. They change and stretch socially in order to inject some new blood into their network.
This one often comes up in the context of a job. Someone may be motivated to achieve something artistically or creatively, but in order to do that they have to work with other people. Maybe they want to get an ambitious film or game made. For that to happen they'll have to watch how they come across to others, be a good group member or leader, and generally not be difficult and alienate everyone. They realize most people can't get away with being a Difficult Genius, someone who's notoriously unpleasant to work with, but everyone puts up with because they're so brilliant.
Some people work on their social skills because they want status and the benefits that come with it. The first example to comes to mind is students vying for popularity in some high school movie. In this case, 'improving your social skills' may involve some more unsavory, Machiavellian tactics. It's hard to imagine a less-sociable, solitary person obsessing about their status, but it is something that drives some people.