Why do weak acids like ethanol not act as a strong base in water?
There seems to be a misunderstanding: The conjugate of a strong base like EtONa can't be a weak acid, because weak acids, like acetic acid for example, are still quite acidic.


Strong acid (HCl) - very weak conjugate base (chloride anion)
strong base (EtONa) - very weak conj. acid (Ethanol)


A strong acid or base reacts strongly (with water), the resulting conjugate is rather inert, with the equillibrium fully on the side of the latter.


weak acid (acetic acid) - weak conj. base (acetate anion)
weak base (ammonia) - weak conj. base (ammonium)


A weak acid or base just reacts partly towards its conjugate, so does the pure conjugate: They are both rather weak. The equillibrium in an equimolar mixture is rather stable: A buffer solution.

The ideal weak base or acid has a $pKa$ of 7 (in water), that is $1/2$ of the -log ion product of the given solvent. If it's even weaker, the conjugate becomes stronger again.