Why do road bikes have thin tyres?

Road tyres are designed to run as fast as possible on a hard and relatively smooth surface. In these conditions thinner tyres are faster because they are more more aerodynamic and can be pumped to higher pressures which usually reduces the rolling resistance of the tyres.

HOWEVER! After decades getting thinner and thinner, the past few decades have seen the "standard" road/racing bike tyre grow from 19mm to 23mm, and now to 25mm. People running road bikes with 28mm tyres is no longer unusual!

The reason for this shift is the discovery that although wider tyres are less aerodynamic, this can be more than made up for by their lower rolling resistance.