Responsive websites automatically resize the pages depending on what
device you're using to view the website. These are a few good
reasons to convert to responsive web design.
It makes it easier for users to share and link to your content with a single URL.
It helps Google's algorithms accurately assign indexing properties to the page rather than needing to signal the existence of corresponding desktop/mobile pages.
It requires less engineering time to maintain multiple pages for the same content.
It reduces the possibility of the common mistakes that affect mobile sites.
It requires no redirection for users to have a device-optimized view, which reduces load time. Also, user agent-based redirection is error-prone and can degrade your site's user experience.
It saves resources when Googlebot crawls your site. For responsive web design pages, a single Googlebot user agent only needs to crawl your page once, rather than crawling multiple times with different Googlebot user agents to retrieve all versions of the content. This improvement in crawling efficiency can indirectly help Google index more of your site's content and keep it appropriately fresh.
Google began penalizing sites that didn't have mobile versions because the need for mobile versions is growing exponentially.