Aircraft carriers move rearming capacity forward

Why use an aircraft carrier if aircraft can refuel in flight?

Because combat aircraft also expend weapons and need servicing; a carrier moves a rearming and sortie-generation base forward, not merely a fuel source.

Fuel is only one resource an aircraft expends in combat. The carrier's decisive logistical contribution is a mobile place to rearm and regenerate sorties, not simply another way to refuel aircraft. The answer distinguishes reach from sustained combat power.