Narrow tyres have lower 'rolling resistance', and require less power to turn them, thus bestowing improved performance and better fuel economy. Thats why small cars have skinny tyres.
Less strain on steering linkages, axles, CV joints, transmissions and wheel bearings.
Lighter weight puts less load on shock absorbers and improves braking [at least until you start skidding, which may occurr earlier in some conditions, with less rubber on the road].
Narrow tyres have significant advantages in directional stability in loose gravel, mud, slush, snow and ice.
They are less prone to staking or stone-cuts when travelling off-road.
They give you a better ride because you miss more bumps and gibbers.
They give you lighter and more accurate steering.
They cost less.
The spare takes up less space, and is lighter for old farts to manhandle onto a roof-rack.
A mate of mine used to run beetle wheels and tyres on his split-screen kombi 'coz he reckons it made it go faster. Every little bit helped with a 36 hp motor!
The only time you need wide tyres is in soft sand, or drive very fast, or have a couple of hundred horsepower.
Wide tyres only became popular because they look good.
Roger [Beetle], old and to forgetful to be wise.