The main point that is missing here is that when you titrate a weak acid or base, you change that acid/base into its conjugate acid/base. However the conj. base of a weak acid is a weak base, which is the exact reason why when you titrate a weak acid with a strong base, the eq. point has a pH above 7. At the eq. pt, youve added an equimolar amt of weak acid and strong base, which means all of the weak acid is now in its conj. base form, which is a weak base and would raise the pH above 7. The reason why we ignore the fact that the same thing occurs with the strong base (which is converted into a weak conjugate acid) is because the conj. acid of the strong base is so incredibly weak it can be ignored.
Absolutely right on the mark in terms of titration. The equivalence point is the point where the reagent initially in the flask has been neutralized by the reagent being added.
Anyway, this explains why you can't titrate a weak acid with a weak base. Although they would neutralize each other, since they both have weak acid/base conjugates, those conj. could also react (essentially the reverse rxn). Thus the titration would not show a clear jump in pH from the eq. pt.
They cannot truly neutralize one another as the word
neutralize is defiened. To neutralize, you must fully consume the other species. By mixing a weak acid (HA) with a weak base (B-), you will get a solution that is a mixture of HA, A-, HB, and B-, with the equilibrium shifted to the side of the slightly weaker reagents (the weaker of the two acids will be on the same side as the weaker of the two conjugate bases), but because they are all weak reagents, they can each assume some concentration that is measurable. Again, it's semantics, but just as a strong acid is defined as one that
fully dissociates, neutralization is defined as
fully consumed. It is generally accepted convention in all general chemistry books that a weak acid cannot fully neutralize a weak base.
You are definitely right that there will be a reaction of some sort, but the magnitude will depend on the relative strengths of the species. It could highly favor one side of the equilibrium, but never 100%. A great way to think about this is to start with a diprotic acid at its first equivalence point. The first proton is esentially completely dissociated and the second proton essentially completely bound (again the exact amounts will depend on the relative strengths of those two particular protons). While the addition of a weak acid or a weak base will shift the equilibrium, it cannot take the diprotic acid all the way to its fully protonated state or to its second equivalence point. Only a strong acid or base can take it all the way to one of those two points.