The definition of competitive inhibition is a "competition" for the active site. At a high enough concentration, the substrate out-competes the inhibitor for the active site, so all enzyme molecules can still bind substrate and reach Vmax. The apparent Km is increased, but Vmax is ultimately unchanged.
The definition of competitive inhibition is a "competition" for the active site. At a high enough concentration, the substrate out-competes the inhibitor for the active site, so all enzyme molecules can still bind substrate and reach Vmax. The apparent Km is increased, but Vmax is ultimately unchanged.