There are several misconceptions being perpetuated with this thread. I think much of it stems from the use of the word neutralize in general chemistry.
To neutralize something does not mean to make it pH = 7. To neutralize a base (strong or weak), you have to add an equal number of moles of strong acid. Likewise, to neutralize an acid (strong or weak), you have to add an equal number of moles of strong base. So neutralize refers to the quantity of the titrant, not the strength.
Second, if we mix equal mole quantities of strong acid and strong base, the pH is 7 given that they perfectly cancel one another and give water and an inert salt. NaOH + HCl leads to NaCl in H2O. But, if we mix a weak acid (such as HF) with an equal mole quantity of strong base, the pH is greater than 7 given that the base is stronger than the acid which forms water and a basic salt. NaOH + HF leads to NaF in H2O. This is why the pH at equivalence point is greater than 7 when a weak acid is titrated by a strong base. Likewise, the pH at equivalence point is less than 7 when a weak base is titrated by a strong acid.
To understand the topic discussed so far in this thread it is critical that you work from the definitions of the words (1) neutralized, (2) equivalence point, and (3) weak/strong.