"This sort of statement sounds suspicious to me. Are you absolutely sure your meaning of introvert isn't idiosyncratic?"The problem is that there are a number of different ways to categorize an extraversion-introversion spectrum, and on top of that, there are many different connotations of introversion and extraversion. It might help if I clarify which definition I'm referring to. It's not very idiosyncratic; rather, it's the classical definition of introversion as "primarily interested in, or taking pleasure in, solitary activities." Occasionally this is rendered as a locus-of-energy distinction: extraverts derive energy from social situations and "tire" of isolation; introverts derive energy from alone time and "tire" from too much social interaction.
Modern connotations of introversion tend to conflate introversion with shyness or awkwardness. While these traits can be correlated, they are not the same thing as introversion.
"If someone wants to be alone, there is absolutely nothing non-genuine about that desire"
Nor did I say there was. I'm just stating that desire to be alone is often at odds with one's ability to keep friendships active and thriving. It's not wrong to be alone, or to want to be alone. But the introvert needs to be mindful of this desire, particularly to whatever extent it interferes with conflicting goals, such as wanting more friends. In this case, the author specifically stated a desire to make more friends. So I wrote from the presumption of that intent.
I'm not rendering any value judgments about introversion or extraversion here. It's not "wrong" to be introverted, or to derive mental or emotional stimulation and energy from being alone. As I mentioned, I myself am a strong introvert in this respect. I don't think I'm a damaged or flawed individual because I'm introverted. Rather, I'm mindful of the fact that my introversion, if I always give into it, can cause problems for my social life. And so I attempt to moderate it, as I do with any of my strong personality traits.
"Different people also want different things from friendships. So if there are two friends, and one sees hanging out as only the means to establishing a deeper intimate friendship, but hanging out and having fun is the main purpose of the friendship to the other, then that's not such a great friendship."
Sure, but that doesn't change the basic facts of social interaction, such as frequency and proximity. You need to interact on a regular basis with someone to maintain a friendship, regardless of what you enjoy doing in that friendship. It doesn't matter if the friendship is predicated on grabbing beers, having deep, philosophical discussions, building things together, traveling, or having sex. At its most basic level, the friendship depends on N encounters over an X period to remain stable. N and X might differ for different pairings of people, but some number N and some recurring interval X usually exist.