Responsive websites are the future today. Did you know that there is over 50% active unique mobile users in the world(mostly of them are using their smartphone to checking the network)? And 11,8% of websites in worldwide network use a responsive web design. That’s a lot!
As you can see, probably mostly of your clients will be using a mobile for checking your website. This is a big argument for you! Websites adjusted for mobile or tablet are also much more friendly for SEO, cause google prefers responsive web design.