Responsive Doesn't Mean Mobile First
There is a lot of confusion these days about Responsive and Mobile First design. While they do work hand in hand, they are not one in the same. Just because your website is Responsive doesn't mean it was built with a priority on Mobile First design.
Here's how it usually works. A company has a desktop design and they get somebody to make it responsive (Responsive Retrofitting as seen in the image). It's understandable. For large corporations, a redesign from the ground up could be very costly and time consuming. The issue is, this doesn't solve any problems for other devices and leads to worse user experiences throughout anything that's not a desktop computer. While it does provide a better experience on mobile than a standard desktop site, there is so much more that can be done to increase the experience across a range of screen sizes.
When you start with a mobile-first design, well, I think Brad Frost says it best:
Mobile-first responsive design is creating an interface that addresses the constraints of mobile (small screen, low bandwidth, etc), then progressively enhances the experience to take advantage of available screen space, features, and more.Brad Frost
Many of us have been using desktop computers for so long, it's hard to let go of all that glorious real estate. We have to get used to the fact that tiny little devices are killing out 30 year paradigm shifters and shifting their own paradigms into the now, and the future, of communication. The sooner you start with mobile first design, the better you will be. As it matures and grows, you will mature and grow. It's tough to change your way of thinking, especially when it's been one way for so long, but you don't want to get left behind.
It will be quite interesting to see what happens to the web and apps as we move forward into smaller devices, wearables and HUD's. The mobile future is here, if you're not already thinking heavily about it, you should be, preparation is key.