I use React because it is well engineered, has a huge community behind it, and allows for modular development (allowing you to handle state management yourself). I've been using React since before 1.0 (or whatever number it was they chose after 0.X). Having said this, I'm not saying other UI libraries are worse. I've barely used the other two big ones.

If using React with a non-trivial application, I heavily recommend using Redux for state management. There is no awful magic or convoluted workflow to Redux (you might not think so when starting on it, but once the light comes on, I hope you'll agree). It's all just loosely coupled state management. Remember to export your connected components separately so you can unit test the component without redux.