For a road bike, you want to minimize the contact area of the tire with the road so you have very narrow tires and inflated a lot so that they don’t deform much under your weight.

It’s slightly different:

• As the top speed of a road bike makes air resistance (drag) an important factor, road bikes use narrow tyres, resulting in a smaller silhouette area than a wide tyre (on a rim of the same diametre) would have.

• As the rolling resistance increases with the length of the contact area, with the same internal pressure (inflation), i.e. same area of contact, narrow tyres have a higher rolling resistance than wide tyres. Thus, to (over-)compensate and decrease the length of the area of contact the internal pressure of road bike tyres is much larger than of normal, wider tyres.

As a result, narrow tyres of road bikes have smaller drag and due to over-compensation by inflation an even lower rolling resistance than standard bike tyres.