Because the amount of total intoxicant is the same.

Let:

A = amount of ethanol

V = initial whiskey volume

W = added water

Initial concentration: c₁ = A / V

After dilution: c₂ = A / (V + W)

If you drink the entire diluted glass: ethanol consumed = c₂(V + W) = A

Intoxication ∝ ethanol consumed

Therefore: drunkenness ∝ A not ∝ (V + W)

Adding water changes concentration, not the total ethanol: A = constant ⇒ drunkenness = constant (ignoring effects of drinking rate).