.if i understand the question correctly, i would say that electron withdrawing groups (EWGs) destabilize carbocations because in general EWG take electrons away from close sources. This weakens bonds. The closer an atom is to an EWG, the more strongly it feels the pull. Since, carbocations are by definition positive carbons, and carbons prefer to be neutral, when electrons are taken away (i.e. some of the negative charge that is helping to balance out the carbocation is taken away) from an already positive carbon, the carbon becomes even more positive still. This ..destabilizes its bonds as well as ..increases the likelihood that this area could react (attacked by a nucleophile).
Acidity is affected in the same manner; the electrons on a -CH3 bond for instance pulled towards an EWG, means that the C-H bond holding the H's in place are less strong. I seem to recall when taking orgo that there are charts that show the relative strength of various groups and show how they affect acidity. .