1) Used and recommended by Google.
A seen on varies blog posts on Google’s official Webmaster Central Blog, Google uses and also recommends using responsive web design. If Google uses and recommends it, are any further reasons required?
2) Saves development and maintenance time
Responsive websites adjust to any screen size and resolution. This saves time in the long runs as device specific versions are not required. Very little maintenance is involved, where as having a mobile specific site would require both versions be updated.
3) Easier Sharing and linking
Having only one url for a page makes it easier to share and link. You are not forced to see a version that is made for mobile on your desktop and vice versa.
4) Better SEO and Analytics
Only one view for the seo and analytics data. One link per post means spending less time shaping and tracking traffic. Add that with Google Analytics and you know exactly what devices your readers are using.