I think the biggest reason to use React is how it handles the DOM. In most framework views, DOM access is slow and can be a bottleneck. React addresses that problem by using a virtual DOM. In order to make a change to the real DOM, React computes a diff between the newly virtual DOM and the previously computed virtual DOM, and then it applies the diff to the real DOM. The triggering to the virtual DOM computation is done explicitly, hence React has a lot better DOM rendering performances.
Everything you can do in React, you can do with other frameworks (Angular's directives and isolated scopes for example), but React is a lot faster and easier to learn, and definitely worth looking into.