Here's what rhymes with evasiveness.

Consider these alternatives

obfuscation / education dogmatism / given discouragement / encouragement inflexibility / stability untruthfulness / usefulness prevarication / education vacillation / relation obliviousness / lasciviousness incapability / ability didacticism / position nonchalance / response hesitance / residence acquiescence / presence ingenuousness / strenuousness unsuitability / stability scrupulousness / unscrupulousness inscrutability / ability