Our goal with React is to make it the best way to build apps on any platform. We've advertised "Learn once, write anywhere" because we do think it's important to put care into each platform you build apps for, but it's silly that you need to relearn everything when switching between web and native – or even between iOS and Android.
Over time, we've realized that even if you make a specialized app for each platform, there are still many parts that should be shared across platforms. All of the model logic is likely the same, and even view logic and appearance is often identical for most of the inner views in an app. So we want to make it easy to share code that should be shared. Facebook's Ads Manager app is built 100% in React Native for both iOS and Android, and we were able to share 90% of the code across platforms. That's huge compared to the status quo of completely rebuilding your app for each platform.
Over time, maybe we can share view code between native and web too. There are some cool projects in the community like react-native-web (https://github.com/necolas/react-native-web) which try to make this possible. We don't have anything to show at Facebook yet down this road but maybe in a year or two we could officially support using View, Image, and Text on the web for people who want to.