There are two main reasons for writing under your own name.
The first is that it holds you accountable. When people write under their own names, they know that they can be blamed or praised for what they write. So, writing under your own name makes you try to be more careful (to avoid embarrassment) and more innovative (to win acclaim).
The second reason to write under your own name is that doing so allows a society to have a clear sense of what its members think. When a society knows what its members think, this better promotes conversation: the more people of different views are willing to stand behind their ideas, the more others want to get in on the action as well. By contrast, widespread pseudonymity not only makes it harder for people to know what their fellows think, creating confusion, it also makes you less trusting of your peers and more alienated.
But sometimes things get out of whack. Right now, we’re either blaming or praising too much, at least when it comes to discussions around race, sex, gender, disability, and politics. Too much of the time, people are willing to go nuclear when you say something about one of these issues that they disagree with. And by the same token, too many people over-praise unimaginative repetitions of their side’s conventional wisdom.
So, writing under your own name nowadays makes you more careful to avoid upsetting people and less careful about whether your reasoning is any good. Disproportionate blame and cheap affirmation encourage intellectual conformity. This, in turn, leads to widespread dishonesty: people are increasingly lying about what they really believe, creating confusion and paranoia.
This is where pseudonymity comes in. Pseudonymity gives you some protection against blame: because it makes it harder for people to discover who you are, it makes it harder for them to denounce you. Thus, though pseudonymity can often encourage careless writing (people won’t find out who you are, so why not try to get away with murder?), it can also, in the right conditions—our current conditions—encourage more careful writing (people won’t find out who you are, so you don’t have to worry about mouthing the day’s social pieties).
Writing under a pseudonym can also make us less worried about proposing new ideas. This is because the pseudonymous writer can not only take greater risks (his pseudonymity protects him) but also because he is less susceptible to the blandishments of cheap praise (the most you can praise a pseudonymous person is through statements of support, rather than actual financial or social currency). Moreover, because the pseudonymous person can choose to unmask, if she lands on winning ideas, she can reveal herself and get properly rewarded.
Consequently, though it’s true that healthy intellectual cultures are better served by people writing under their own names (this is called onymous writing), it’s also true that sick ones can be better served by pseudonymity. Since our intellectual culture is sick, it’s at least defensible to write pseudonymously. It may even be better.