What ever happened to good old fashioned resonance?
In the -CN cases, the carbon has three bonds pulling electron density away by the inductive effect, and two pulling electron density away by resonance, therefore it's highly withdrawing. In the -COOH case, the carbon has three bonds pulling away by the inductive effect, one pulling away by resonance and another
donating by resonance, therefore it's mildly withdrawing. The difference here is due to resonance.
LoveofOrganic gave a great example where only inductive effect was applicable, and the additive effect was right on the mark. When it's the inductive effect only, additive does work out, exactly as he (or she) said. You countered with an example showing that the additive approach doesn't work in some cases, where the fundamental reason was because of resonance. The argument is not who's correct (given that you both are), but "when do you consider resonance versus when do you consider the inductive effect?"
Let's come up with a general set of rules to explain acidity.
- Relative acidity rules
1) EWGs increase acidity and EDGs decrease acidity
2) Resonance is more important than inductive effect
3) For resonace, EDG have lone pairs that can be shared into the pi-system. EWG have pi-bonds that can pull away electrons from the atom with the protic hydrogen.
4) For the inductive effect, proximity (distance from the protic hydrogen) and quantity (the more electronegatiove atoms present, the greater the effect) impact its strength.
Please pile on more and build the list.