I can't connect with others. (Closing points)

Well I'm certainly an introvert, and a pretty extreme one at that.  Dealing with other people almost never seems like something enjoyable to do.  Of course there are exceptions.  I can't say that I've never enjoyed talking with other people, or that there is no one who I enjoy being around.  But still, it's so extreme, like, if I were to say, "Have you ever played some kind of game, a board game, video game, you name it, and enjoyed it?" and you say yes, and then I say, "So, you can see why there are people who could play the same game a hundred hours, or a thousand hours, their entire lives even, because they really enjoy it, right?" and unless you're actually into games you say, "Uh, no not really."

With a quick search you could find out all kinds of stuff about introverts.

Introverts tend to dislike small talk.

Well, I can say that this one fits me.  Most of what could be called "small talk" is stuff that I'm not interested in saying, and not that interested in listening to.  I guess extroverts just ask these questions that other extroverts have long responses to, and they expect people to go on and on with an answer to a question like, "How are you today?" but all I have to say is, "Fine," "Good," or something.  "Well."  If you wanted to know something more, you'd have to ask about it specifically, because all I would really be interested in knowing is stuff like, "Are you still alive with no major injuries and no huge difficulties to face and you haven't won the lottery or anything?" so really that's all I'd be answering.  "I'm still alive and well and I have nothing else to add unless you have something else to ask."

Introverts need time alone to recharge.

 I see this a lot, but I've never seem myself like that.  Maybe if you looked at my "social battery" like a terrible laptop battery, you know, the kind that runs out in a couple minutes, then I could see it.

Myth #2 – Introverts are shy.

The not shy introverts say that just because you're introverted doesn't mean that you're shy, which is surely true.  But just because there are introverts that aren't shy doesn't mean that all introverts aren't shy.

Myth #4 – Introverts don’t like people.

On the contrary, Introverts intensely value the few friends they have. They can count their close friends on one hand. If you are lucky enough for an introvert to consider you a friend, you probably have a loyal ally for life. Once you have earned their respect as being a person of substance, you’re in.

I guess you could say I'm even more accepting of others than most.  I mean, in general I would say that I've got nothing against other people, and I don't care if you don't see the world in the way that I do.  But I probably won't say much to you because I just don't have much to say period.

Myth #1 – Introverts don’t like to talk.
This is not true. Introverts just don’t talk unless they have something to say. They hate small talk. Get an introvert talking about something they are interested in, and they won’t shut up for days.

 I've got to believe that this is the best way to talk to introverts.  If you can find what they want to say and show that you're genuinely interested in hearing what it is they want to say, well I'd imagine that it would make for a good conversation.  That would probably be an excellent way to talk to other people in general anyway, introverts or extroverts.
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So, the next thing would be, "What is it that I want to say?"  Well why would I tell you that?  So you can tell me that you don't see the point in talking about something like that?  So you can say, "Oh, thaaat's what it is that you enjoy talking about." in some extremely judgmental tone?

Yeah, I do feel that social anxiety to some extent.  The first paragraph on it in Wikipedia says:

Social anxiety is anxiety (emotional discomfort, fear, apprehension, or worry) about social situations, interactions with others, and being evaluated or scrutinized by other people that is typically characterized by an intense, ego-driven fear of what others are thinking about them (specifically fear of embarrassment, criticism, rejection, etc.), which results in the individual feeling insecure, and that they are not good enough for other people, resulting in intense fear and anxiety in social situations, and the assumption that peers will automatically reject them in social situations.

 I read through it saying, "Yeah, yeah, I guess so," until I get to the part about insecurity and not good enough for other people.  I don't have any doubts about myself, and I would prompt a challenge by saying, "What, you think you're better than me?"  I mean I don't know, surely you are at some thing (you know, like some random thing out there that I'm not that interested in), but I would never consider myself to be "not good enough" for someone.
I don't mind saying that I probably have social anxiety because I've somehow ended up in the ironic position where, if anyone were to say that my way of life or my interests or my desires were just wrong, then a million counterpoints would jump to the forefront of my mind and then I'd actually be making myself feel more at ease instead of making myself worry.  Like, if you actually wanted to make me doubt myself, you'd have to out-logic me (which is already virtually impossible (not because my logic is so good, but because you'd have to find some set of absolute statements which I don't believe exist)), and if I lose some kind of logic battle then it's because I said something that's actually wrong, and it's different being corrected on something that's actually wrong.  Basically it wouldn't be an opinion thing anymore and so I wouldn't be bothered by it.  So yes, I'm saying that if you want to challenge my opinions, go ahead.  In some ways it'd put me at ease, and I have a ton of counters ready, so, good luck.
But the fact of the matter is that it's still there.  I really don't want to hear people telling me how wrong they think my opinion is, and at the same time, I'm not really interested in having my opinion supported.  So not only is there no reason for me to tell other people my opinions, there's actually reason not to.  Which, as you might imagine, greatly limits the amount of things that fall under the category of "things I want to say."
See, I'm virtually always silent on my (very very slight preferences that are so small and vague that they hardly deserve to be called) opinions, so other people really don't know what they are.  Which means that any time a strong negative opinion is expressed on something, it could very well be a strong negative opinion on something that I, you know, care about.  Now with how it is with friends, I'd bet that if, after someone said something like, "Man, who would like something dumb like that?" I said, "Hey, I like that," then the response would go something like, "Well it has this and this which are redeeming qualities," or "Well yeah I guess it's not that bad," etc etc.  Okay, so you were either over-emphasizing the negative points initially (which why would you want to do that?  To make me feel uncomfortable?) or you're softening you're true opinion (which is nice and all, but you already said how you actually feel).  And then the closing point is that, well, maybe I don't actually have an opinion on what you're talking negatively about, but you're still showing that you make negative judgments on people based on their opinions on a given topic, and that almost guarantees that I'll never want to talk to you about my (very very slight preference that is so small and vague that it hardly deserves to be called an) opinion on anything near that topic.  Look it's cool that you have your judgments on things, but I really don't care about making you support what I like, and I really don't want to have to answer questions like, "Well why do you like something like that?" or to have to deal with people saying how awful what I like is.
But it would be how close I am to another person (or, well, every other person that my preference was being expressed to) that would determine how hard it was to express my preference.  And either you were coincidentally similar to me as far as feelings and mindsets and personalities went, or it was a looooong bridge spanning a huuuuge gap.  But, I don't believe any such bridges are truly uncrossable.

The last thing was that it often took me a long time to put together my words.  Sometimes I feel like when people ask me a question I should say, "Wait, give me 15 seconds to organize my thoughts and all, and then maybe I can give a meaningful answer."  And I can already imagine the murmurs of, "Is that a weakness?  A disability?!" and my reply of, "No way, I don't believe in things like that!" as I go on to spend the rest of my life focused on improving my communication skills to show that it was something that could be overcome...  Something like that.