Nothing. Nothing at all. There's nothing wrong with soloing in MMORPGs.
The thing about MMORPGs is that nowhere in the words "massively multiplayer online roleplaying game" is there any sort of mandate about soloing or grouping at all. Massively multiplayer online roleplaying game refers to the scale of people in the world, suggests the virtual location of the game, makes vague promises about playing a role, and that's pretty much it. You'll find lots of people happy to interpret that in a way that suits their personal tastes, however, including those who believe that if you're not grouping with them at all times, you're doing it wrong, you're betraying the genre, and you're spoiling the game.
But you're not. If the game allows soloing, and you enjoy soloing, then you're playing the game in at least one of the ways it was intended, just as everyone else is. The unreasonable expectations of the "group or die" players should have zero impact on you. You don't exist for them or for anyone else; your gametime should make you happy, however you choose to spend it. And for some people, that means soloing in a massively multiplayer world.
The "alone together" catchphrase is particularly applicable to MMOs. Some people love the feel of being in a virtual, persistent space with thousands of other people amidst a story and economy that moves independent of them, something that's just not possible in a single-player game, but they'd still rather do most of their daily game activities on their own. When I go to the mall or an amusement park or museum, I generally don't interact with most of the people I see passing by; I'm there to do my own thing. But an empty mall or amusement park or museum is actually a little creepy. Masses of people define the space and enhance the activity even if I interact with only a few of them personally. So it is in virtual worlds: Sometimes you want to be a part of something massive and awesome and alive but don't necessarily want to become some other gamer's temporary dungeon BFF just to be considered normal.
That doesn't stop some players from measuring an MMORPG's social atmosphere by whether or not people are forced into dungeon grouping, nor does it prevent them from defining social gameplay as something doable only in units scaled to some dungeon party, which is arbitrary and silly. There are plenty of other social activities in games and plenty of things solo players do that are actually quite social. For example, someone who gathers, crafts, buys, and sells on an auction hall is participating in an economy, a very social activity regardless of how indirect it is or whether the participant spends any time furiously typing. In fact, someone who participates in the economy through an auction hall or vendor is touching and affecting far more participants in said economy than someone who merely runs a dungeon with four people. You'll also find solo gamers actively participating in world chats and on forums, dispensing advice while they do their thing in the open world, since some players just feel more comfortable talking to fellow players ad hoc than taking on the pressures of being in a group. My own guild is staffed with a number of players who are most comfortable soloing but still heavily contribute to the festivity and leadership and camaraderie and stockpiles of our team. Even PvP is social!
Consider also that there are plenty of social-friendly reasons to solo. If I'm tinkering in an MMO while keeping an eye on my toddler, there's no way I'm going to jump into a group for a dungeon. I might need to AFK at a moment's notice to clean up a diaper or sippy cup disaster or crumbled LEGO tower, and that'd mean leaving my group in the lurch. It would be actively rude of me to impose on my groupmates, knowing I couldn't fully commit to the activity. The social, as opposed to anti-social, thing to do in that situation is stay solo. An anti-social person would just join a party, loot some stuff, and leave without a thought for other gamers, and yet since he is grouping rather than soloing, far too many people would consider him the social one.
And let's not forget that MMOs provide an outlet for introverts to interact in a big virtual world on their own terms without the pressures they might face in the real world. There's nothing wrong with being shy, in-game or out, and there's nothing pathological about introversion, the same way there's nothing pathological about extroversion. (Most people are a little bit of both in different situations; I'd wager, for example, that most extroverts who read Massively aren't big proponents of social games or social media.) Extroverts already benefit wildly from MMORPG game design. They will always be in the biggest guilds and have the longest friends lists and get into the best raids. They have such a distinct innate advantage that it's frankly cruel for them to tell shybies to group up or go away and stop ruining "real" MMORPGs. That's the attitude most gamers come to MMOs to escape.
I won't claim that our genre never sees "massively singleplayer" games or even that we're not in the midst of a "mingleplayer" gamevalanche. A lot of modern MMOs and pseudo-MMOs are little more than singleplayer grindparks with combat lobbies and a chat channel slapped in to produce an extra revenue stream for a company. But they aren't the only games being produced, and they do serve as a gateway drug for potential players of truly massively multiplayer games, which means more players and more money for our corner of the industry -- yes, even some gamers who don't agree that a 5-man dungeon is the end-all, be-all of socializing. There will always be legit MMORPGs with dungeon grouping as one avenue for being social. We just need to recognize that there are lots of other social activities too, and the best MMOs will include more and more of them, not fewer in some attempt to reclaim EverQuestian glory days.
The MMORPG genre might be "working as intended," but that doesn't mean it can't be so much more. Join Massively Editor-in-Chief Bree Royce every other Friday in her Working As Intended column for editorials about and meanderings through MMO design, ancient history, and wishful thinking. Armchair not included.