Software companies are all about lock-in, controlling the platform, making sure they have control of as much user and dev attention as possible. At Facebook's world-eater size, the better question is "Why should we not seek to dominate this element of the development platform?"

I can't pretend to know the exact rationale behind Facebook's decision to open-source React, but there are several things to gain from controlling a major piece of the web infrastructure: influence/clout with browser vendors (decisions that may negatively impact React's performance now threaten a huge percentage of the web, not just Facebook.com), the ability to introduce more and more Facebook-controlled technology with something like React as a shoehorn ("You liked React, try Flow..."), PR benefit/good vibes, and so forth.

Platform control is the real showdown among big software companies. It makes your company downright inextricable. Just ask Microsoft.