Great question. This was something we thought about a lot.
Some social networks have taken the position that requiring real names reduces the potential for abuse, based on the theory that people are less likely to be jerks if everyone knows who they are. But this assumes that you have the ability to verify that someone is who they say they are, which is surprisingly difficult to do. It also assumes that everyone actually uses (or wants to use) their legal name in public life, which isn't always true.
Real name policies can also have the unintended drawback of silencing people who are more likely to be targets of abuse or harassment online. Women, people of color, and LGBTQ people are frequently targeted online, and are sometimes harassed in person for things they say online. Being required to use their legal names forces them to choose between risking their physical and mental safety or simply being silent, meaning they often choose to be silent. We definitely don't want that.
And then there's the fact that some people just want to be able to talk freely about certain interests online without worrying about what other people (friends, coworkers, etc.) will think of them. If I want to nerd out on Cake about knitting but I'm a little embarrassed because it's not usually considered a very masculine hobby, I should feel free to create an account that's not associated with my real name so that I can talk about knitting to my heart's content.
We realize that, inevitably, there will be people who will abuse anonymity and be jerks, but we're confident that the benefits ultimately outweigh the drawbacks, and we have systems in place to help us deal with abuse if and when it becomes a problem.